Systems and methods for particle focusing in microchannels

ABSTRACT

Various systems, methods, and devices are provided for focusing particles suspended within a moving fluid into one or more localized stream lines. The system can include a substrate and at least one channel provided on the substrate having an inlet and an outlet. The system can further include a fluid moving along the channel in a laminar flow having suspended particles and a pumping element driving the laminar flow of the fluid. The fluid, the channel, and the pumping element can be configured to cause inertial forces to act on the particles and to focus the particles into one or more stream lines.

RELATED APPLICATIONS

The present application claims priority to U.S. Provisional ApplicationNo. 60/923,609 filed on Apr. 16, 2007 and entitled “Methods and Devicesfor Separating and Focusing Particles,” U.S. Provisional Application No.60/923,837 filed on Apr. 17, 2007 and entitled “Methods and Devices forSeparating and Focusing Particles,” and U.S. Provisional Application No.60/999,131 filed on Oct. 16, 2007 and entitled “Methods and Devices forSeparating and Focusing Particles,” all three of which are expresslyincorporated herein by reference in their entireties.

BACKGROUND OF THE INVENTION

Particle separation and filtration has been applied for numeroustechnological solutions in industry, medicine, and research. Industrialapplications include chemical process and fermentation filtration, waterpurification for the microelectronics industry, and wastewatertreatment. Biomedical applications focus around counting, sorting andfiltering various components of blood and preparing safely sizedmicro-bubble ultrasound contrast agents. Applications in basic andapplied research include concentrating colloid solutions, purifyingcolloidal reaction products, and purifying and concentratingenvironmental samples.

Various macroscale techniques have been developed for particleseparation to address these applications. Centrifugation andfilter-based techniques are most common in current industrialapplications because of the large scale of material that can beprocessed, but these systems are bulky, expensive, and may containcomplex moving components. More recently, techniques based on theconcept of field-flow fractionation (FFF) have been developed for avariety of applications. In these techniques, particle separation is dueto either varied equilibrium positions within a channel in an appliedforce field or different transport rates. Various external fields havebeen implemented including gravitational, electrical, magnetic, andcentrifugal, allowing successful separation of blood components,emulsions, and various colloids. A closely related technique,hydrodynamic chromatography, is also widely used in analyticalseparations and depends on size-dependent variation in the ability ofparticles to access low-drag regions of the flow. In most cases, themaximum flow through these systems is limited since sufficient time forforces to interact with particles or particles to sample the flow fieldis required. Flow cytometers are often used in sorting applications andallow sorting based on different parameters than other techniques (e.g.,protein content, granularity); however, they have higher complexity thanmost sorting systems.

Microscale techniques offer advantages, in that scaling down allows theuse of unique hydrodynamic effects and intensifies electromagneticseparation forces. Dielectrophoretic forces have been used todiscriminate particles based on size or some dielectric tag. Othertechniques for continuous separation rely on the laminar flow profileand different intersected cross sections of the flow for particles ofvaried sizes aligned at a wall. Further microscale techniques involveprecisely designed filters or post arrays that create a bifurcation inparticle direction based on size. These techniques can produce veryaccurate separations based on size or the dielectric properties ofparticles. For example, for deterministic displacement by asymmetricallyaligned obstacles, a resolution of less than 20 nm is reported forparticles of ˜1 μm in diameter. Additionally, complexity can be low inthese systems.

A disadvantage of current microscale separations is that scaling usuallylimits the throughput of these techniques. In most cases, particlevolume fractions are maintained well below 1%, since particle-particleinteractions can drastically affect performance. Additionally, smallvolumetric flow rates can lead to large average fluid velocities inmicrochannels leading to insufficient time for separation forces to acton particles. Flow rates usually range from 1 to 50 μL/min for thesesystems, insufficient for many preparative applications (e.g.,concentration of rare cells in large volumes of blood, filtration ofultrasound contrast agents, or preparation of large amounts ofcolloids/emulsions). In these applications, it would be beneficial toprocess volumes of 3-20 mL within several minutes. For example, 2-6 mLof micro-bubble contrast agent is often injected for ultrasound imaging.

Accordingly, there is a need for a continuous particle sorting,separation, enumerating, or separation system that can take advantage ofmicroscale physics but with throughput comparable to macroscale systems.

SUMMARY OF THE INVENTION

The invention described herein includes a number of systems, devices,apparatus, and methods that result in and use the self-ordering ofparticles suspended in a fluid traveling through a microfluidic channel.In a first aspect, a system is provided for focusing particles suspendedwithin a moving fluid into one or more localized stream lines. Thesystem includes a substrate and at least one channel provided on thesubstrate having an inlet and an outlet. The system further includes afluid moving along the channel in a laminar flow having suspendedparticles and a pumping element driving the laminar flow of the fluid.The fluid, the channel, and the pumping element are configured to causeinertial forces to act on the particles and to focus the particles intoone or more stream lines.

In another aspect, a method is provided for focusing particles in amoving fluid and includes providing particles suspended in a movingfluid into a channel and flowing the fluid through the channel underconditions such that inertial forces acting on the particles result inthe localization of a flux of particles in the channel.

In a further aspect, an apparatus is provided for focusing particles ofa predetermined size suspended within a moving fluid into one or morelocalized stream lines. The apparatus includes a substrate and at leastone channel provided on the substrate having an inlet and an outletwherein moving a fluid suspension having particles of a predeterminedsize from the inlet to the outlet in a laminar flow focuses theparticles of a predetermined size into one or more localized streamlines.

In a still further aspect, a system is provided for sorting particlesfrom a group of particles suspended in a fluid and includes a taggingsystem for tagging particles that are to be selectively sorted from agroup of particles. The system further includes a substrate having atleast one channel provided on the substrate having an inlet and anoutlet. Moving the fluid suspension having particles, at least some ofwhich have been tagged, from the inlet to the outlet in a laminar flowfocuses the particles into one or more localized stream lines. Theoutlet can have at least two output branches, the first of the twooutput branches for separating the particles to be sorted, and thesecond of the two output branches for outputting the remainder of theparticles that have not been segregated. The system can also include asorting system operatively connected to the channel for selectivelydiverting particles to the first output branch.

In a final aspect, a method is provided for separating target particlesfrom a population of particles and can include providing a population ofparticles, including target particles, in a fluid suspension and flowingthe fluid suspension through at least one channel under conditions thatcause at least some of the particles to form a localized flux ofparticles in the channel. The method can further include dividing anoutput from the channel into first and second output branches in whichthe output branches are configured so that the second output branchreceives a flow that is enriched in target particles while the firstoutput branch receives a flow reduced in target particles.

Specific embodiments of any of these aspects can include moving thefluid suspension can focus the particles into four localized streams,two localized streams, and/or a single localized stream. The channel canhave a hydraulic diameter and a ratio of a size of the particles focusedto the hydraulic diameter that is greater than or equal to about 0.07.The ratio of particle size to hydraulic diameter can be less than orequal to about 0.5. In some embodiments, a Reynolds Number of the fluidflow during focusing can be greater than or equal to about 1 and lessthan or equal to about 250. In some embodiments, a particle Reynoldsnumber for the fluid suspension moving through the channel is greaterthan or equal to about 0.2. The one or more focused stream lines canhave a width that is less than or equal to about five times, four times,three times, two times, and/or 1.05 times a size of the focusedparticles. Embodiments of the system can increase the concentration ofparticles in solution.

In the enumerated aspects or in any of their embodiments, at least firstand second outlet branches can be formed at an outlet portion of thechannel and at least one of the first and second outlet branches can belocated on the substrate so as to receive the particles from a focusedstream line and/or from the single localized stream. In someembodiments, the channel can have a rectangular cross-section. In otherembodiments, the rectangular channel can have a width of less than orequal to about 1000 micrometers, 650 micrometers, 100 micrometers, 80micrometers, 65 micrometers, 50 micrometers, 20 micrometers, and/or 10micrometers.

In any of the aspects, embodiments can include those in which particlesare cells, including mammalian cells, blood cells, tumor cells, and/orbacteria cells. In addition, the aspect ratio of the rectangularcross-section can result in the focusing of particles into two streams.Focusing of particles into one or more localized stream lines can spacethe particles approximately evenly longitudinally. In some embodiments,the aspect ratio of a first rectangle dimension to a second rectangledimension can be between approximately 0.3 and 0.8. In otherembodiments, the aspect ratio can be approximately 1 to 2.

In the enumerated aspects or in any of their embodiments, the system caninclude at least one channel that curves and is symmetric and sigmoidal.In other embodiments, the channel can be asymmetric and sigmoidal. Thelocation of the focused stream within the channel can depend uponinertial forces and Dean drag forces acting on the particles. Thelocation can further depend upon centrifugal forces acting on theparticles. A Dean number for flow through the channel can be less thanor equal to about 20. In some embodiments of the system, the radius ofcurvature can vary and/or can change after each inflection of the curve.A cross sectional dimension of the channel can vary and can change aftereach inflection of the curve. In one embodiment, the channel can form aspiral.

In other embodiments, a plurality of channels can be provided on thesubstrate and at least some of the channels can be configured to allowserial flow. A plurality of channels can be provided on the substrateand a first channel can have first and second output branches leading tosecond and third channels respectively. At least two of the channels canbe configured to focus particles of different predetermined diameters.The system can include a detector for detecting and enumeratingparticles in the one or more focused stream lines and for detecting andenumerating particles in the single localized stream. The system canfurther include a tagging system for tagging selected particles with atag that can be detected by the detector, the detector thereby detectingand enumerating the selected particles. In any and all aspects,embodiments can include systems in which the focusing can resultexclusively from the inertial forces. Other embodiments can includesystems in which the focusing can result from inertial and other forces.

In any of the aspects, further embodiments can include methods forfocusing particles in which the fluid flow through the channel islaminar and wherein the Reynolds Number of the fluid flow is betweenabout 1 and 250. Focusing can produce a localized flux of particlesenriched in a first particle based on particle size. A first particlediameter divided by a hydraulic diameter of the channel can be greaterthan or equal to about 0.07 and the first particle diameter divided bythe hydraulic diameter of the channel can be less than or equal to about0.5. In some embodiments, the channel has a rectangular cross-section, aheight, a width, and a hydraulic diameter equal to2*height*width/(width+height) and the rectangular cross-section has anaspect ratio of between approximately 0.3 and 0.8 and/or approximately 1to 2.

In the enumerated aspects or in any of their embodiments, methods forfocusing particles can include applying an asymmetric force to theparticles to produce one to three localized fluxes of particles. Theasymmetric force can include, but is not limited to, centrifugal,hydrodynamic drag, electrical, magnetic, thermal, sonic, optical, ordielectrophoretic forces. In some embodiments, the asymmetric force caninclude a Dean drag force that is equal to or greater than about 0.5 nN.Particles can include, but are not limited to, cells, beads, viruses,organelles, nanoparticles, and molecular complexes. Cells can include,but are not limited to, bacterial cells, blood cells, cancer cells,tumor cells, mammalian cells, protists, plant cells, and fungal cells.

In any of the aspects, embodiments can also include methods for focusingparticles in which the channel is curved and wherein a Dean number ofthe moving fluid is less than or equal to about 20. The curved channelcan be sigmoidal and/or spiral. In other embodiments, the curved channelcan be sigmoidal and asymmetric and the radius of curvature can varyfrom one inflection point in the sigmoidal curve to a next inflectionpoint in the sigmoidal curve. In some embodiments, a first radius curvecan be followed by a larger radius curve. The first radius curve canapply a Dean drag that is about eight times greater than a Dean dragapplied in the larger radius curve. In other embodiments, the channelcan have a rectangular cross-sectional shape and at least one dimensionof the rectangular cross-sectional shape can vary from inflection pointto inflection point in the sigmoidal curve.

In the enumerated aspects or in any of their embodiments, methods forfocusing particles can include passing the moving fluid from the channelinto at least two output branches wherein one of the output branches islocated so as to receive the localized flux of particles enriched infirst particles of a given size. Receiving the localized flux canthereby increase the concentration of first particles in solution. Insome embodiments, the method can include passing the moving fluid fromthe channel into at least two output branches wherein one of the outputbranches is located so as to receive the localized flux of particlesenriched in first particles of a given size. A detector can be appliedto enumerate particles traveling in the localized flux of particles inthe channel. Methods can further include a tagging system for taggingselected particles with a tag that can be detected by the detector, thedetector thereby detecting and enumerating the selected particles. Inany and all aspects, methods can include systems in which the focusingcan result exclusively from the inertial forces. Other methodembodiments can include systems in which the focusing can result frominertial and other forces.

In any of the aspects, embodiments can include an apparatus wherein thecross sectional shape and area of the channel can be consistent from theinlet to the outlet. In other embodiments, the cross sectional shape andarea of the channel can vary from the inlet to the outlet. The one ormore localized stream lines can have a width that is less than or equalto about five times, four times, three times, two times, and/or 1.05times the predetermined particle size. Moving the fluid suspensionhaving particles of a predetermined size from the inlet to the outletfocuses the particles of a predetermined size into four localizedstreams, two localized streams, and/or a single localized stream.

In the enumerated aspects or in any of their embodiments, the apparatuscan further include at least first and second outlet branches formed atan outlet portion of the channel, at least one of the first and secondoutlet branches being located on the substrate so as to receive theparticles of a predetermined size from the single localized stream. Insome embodiments, the aspect ratio of the rectangular cross-sectionresults in the focusing of particles into two streams. Further, thefocusing of particles into one or more localized stream lines can spacethe particles approximately evenly longitudinally. In other embodiments,the location of the focused stream depends upon inertial forces and Deandrag forces acting on the particles. The location can further dependupon centrifugal forces acting on the particles.

In any of the aspects, embodiments can include an apparatus wherein across sectional dimension of the channel varies. In some embodiments,the cross sectional dimension of the channel changes after eachinflection of the curve. A plurality of channels can be provided on thesubstrate and can be configured to allow parallel flow. In otherembodiments, a plurality of channels can be provided on the substrate,and at least some of the channels can be configured to allow serialflow. A plurality of channels can be provided on the substrate and afirst channel can have first and second output branches leading tosecond and third channels respectively. At least two of the channels canbe configured to focus particles of different predetermined diameters.

In the enumerated aspects or in any of their embodiments, the system canfurther include a tagging system that can be a passive sorting system.The tagging system can apply to the particles to be segregated a taghaving a property that can be forced out of the focused particle streamby the sorting system. The tag can increase the particle size and thesorting system can include a channel geometry that segregates particlesinto the first and second output branches based upon size. In someembodiments, the tag can include a magnetic property and the sortingsystem can include a magnetic biasing element that applies a force tothe tagged particles that diverts the tagged particles from the secondto the first output branch. In other embodiments, the tag can include anelectric property and the sorting system can include an electrophoreticforce to the tagged particles that diverts the tagged particles from thesecond to the first output branch. The sorting system can include anaffinity column that diverts the tagged particles from the second to thefirst output branch.

In any of the aspects, embodiments can include a sorting system which isan active sorting system and can further include a controller forselectively diverting tagged particles from the second to the firstoutput branch. The sorting system can further include a detector fordetecting tagged particles, the detector being operatively connected tothe controller to signal to the controller the presence of a taggedparticle for diversion. The detector can be a fluorescence detector andthe tags can be fluorescent tags.

In any of the aspects, certain embodiments of the sorting system canfurther include a channel resistance actuator, the channel resistanceactuator being selectively actuated by the controller to divert taggedparticles from the second to the first output branch. The channelresistance actuator can be coupled to the first output branch to lowerthe fluid resistance of the first output branch to divert a taggedparticle from the second to the first output branch. In someembodiments, the channel resistance actuator can be coupled to thesecond output branch to increase the fluid resistance of the firstoutput branch to divert a tagged particle from the second to the firstoutput branch. The channel resistance actuator can be a microvalve thatpartially opens or closes to change the fluid resistance of an outputbranch. In other embodiments, the channel resistance actuator canstretch or squeeze a dimension of the channel to change the fluidresistance of an output branch. In any of the aspects, the particles canbe cells and the cells can be sorted based upon a property of the cell.In some embodiments, the property of the cell for which it is sorted isthe presence of at least one indicator of cancer.

In the enumerated aspects or in any of their embodiments, methods forseparating target particles from a population of particles can beprovided wherein the dividing is done passively. The target particlescan have a different size than other particles in the population and thetarget particles can form a localized flux in a predetermined locationwithin the channel. In some embodiments, an entrance to the first outputbranch can be located so as to encompass the predetermined locationwithin the channel of the localized flux of target particles.Embodiments of the method can also include selectively tagging particleswith a tag that is used by a dividing system operatively connected tothe channel. The tag can increase the size of the selectively taggedparticles and the tag can be a magnetic tag.

In any of the aspects, embodiments can further include methods whereinthe dividing system employs a magnetic field to direct target particlesto the first output branch and other particles to the second outputbranch. The method can include detecting tags or tagged particles by thedividing system, and diverting by the dividing system of taggedparticles into a selected one of the first and second output branches.The dividing system can include a detector operatively connected withthe channel, a fluid resistance varying element operatively connected toat least one of the first and second output branches, and a controllerin communication with the detector and the fluid resistance varyingelement. In some embodiments, dividing an output from the channel caninclude detecting tagged particles by the detector, communicatinginformation regarding the detection from the detector to the controller,and signaling by the controller to the fluid resistance varying elementto vary the fluid resistance in at least one of the first and secondoutput branches so as to cause the tagged particle to flow into aselected one of the output branches.

In the enumerated aspects or in any of their embodiments, the populationof particles can include, but is not limited to, cells, beads, viruses,organelles, nanoparticles, and molecular complexes. In some embodiments,the target particles can be cells and the channel can be curved. Inother embodiments, the first radius curve of the channel can apply aDean drag that is about eight times greater than a Dean drag applied inthe larger radius curve. The channel can have a rectangularcross-sectional shape and at least one dimension of the rectangularcross-sectional shape can vary from inflection point to inflection pointin the sigmoidal curve.

BRIEF DESCRIPTION OF THE DRAWINGS

The invention will be more fully understood from the following detaileddescription taken in conjunction with the accompanying drawings, inwhich:

FIG. 1A illustrates one embodiment of a system for the separation,ordering, and focusing of particles within microchannels;

FIG. 1B illustrates an example of one microchannel of FIG. 1A;

FIG. 2A is a side-view of one embodiment of a straight channel for theseparation, ordering, and focusing of particles;

FIG. 2B is a cross-sectional view of the straight channel of FIG. 2Ashowing four equilibrium positions for focused streams of particles;

FIG. 2C is a cross-sectional view of an exemplary high-aspect ratiostraight channel showing two equilibrium positions for focused streamsof particles;

FIG. 3A is a side-view of one embodiment of a symmetrically curvedchannel for the separation, ordering, and focusing of particles;

FIG. 3B is a cross-sectional view of the symmetric channel of FIG. 3Ashowing two equilibrium positions for focused streams of particles;

FIG. 4A is a side-view of one embodiment of an asymmetrically curvedchannel for the separation, ordering, and focusing of particles;

FIG. 4B is a cross-sectional view of the asymmetric channel of FIG. 4Ashowing one equilibrium position for focused streams of particles;

FIG. 4C is a perspective view of another embodiment of an asymmetricallycurved channel in the form of an expanding spiral channel;

FIG. 5A is a cross-sectional view of one embodiment of a straightchannel having a rectangular cross-section showing forces acting onparticles within the channel;

FIG. 5B is a representation of the forces acting on a particle withinthe straight channel of FIG. 5A;

FIG. 6A is a parabolic velocity profile of Dean drag forces actingwithin a curved microchannel;

FIG. 6B illustrates Dean flow velocity dependence on Dean number withincurving microchannels;

FIG. 6C is a graph illustrating average secondary flow velocitymagnitude as a function of changing Dean number for a single channelgeometry;

FIG. 7 is a cross-sectional view of one embodiment of an asymmetricallycurved channel depicting the superposition of the four stable positionsdue to inertial lift forces with the Dean flow;

FIG. 8A is a cross-sectional view of one embodiment of a straightchannel showing particles focused into four lateral positions;

FIG. 8B is a side view of the straight channel of FIG. 8A showing theparticles focused into four streams;

FIG. 8C is a side view and cross-sectional view of the straight channelof FIG. 8A showing that the degree of focusing increases with R_(e;)

FIG. 9A is a representation of focusing within one embodiment of ahigh-aspect ratio straight channel, showing focusing to two streams;

FIG. 9B is a representation of particle ordering and spacing within thestraight channel of FIG. 9A;

FIG. 9C is a representation of particle ordering and spacing within thestraight channel of FIG. 9A;

FIG. 9D is a representation of particle ordering and spacing of twodifferent particle types within the straight channel of FIG. 9A;

FIG. 10A is a side view of one embodiment of a symmetrically shapedchannel showing focusing of particles into two streams;

FIG. 10B is a side view of the channel of FIG. 10A illustrating particlefocusing increasing with R_(e);

FIG. 11A is a side view of one embodiment of an asymmetrically shapedchannel illustrating particle focusing increasing with R_(e);

FIG. 11B is a side view of the channel of FIG. 11A, showing a singlestream of focused particles;

FIG. 11C is a cross-sectional view of the channel of FIG. 11A, showingparticles focused to a single equilibrium position within the channel;

FIG. 11D is a side view of the channel of FIG. 11A showing particlefocusing at various locations along a length of the channel;

FIG. 12 is a cross-sectional view of one embodiment of an asymmetricallyshaped, expanding spiral channel showing equilibrium positions thereinfor particle focusing;

FIG. 13 is a side view of the channel of FIG. 12, illustrating particleordering therein;

FIG. 14 is a representation of one embodiment of a system for theseparation, ordering, and focusing of particles having asymmetricalchannels;

FIG. 15A is a representation of one exemplary system and method forpassive particle separation using magnetically labeled particles foridentification in focused streams;

FIG. 15B is a representation of one exemplary system and method foractive particle separation using fluorescence to identify particles of apredetermined type in focused streams;

FIG. 15C is a graphical representation of the frequency of rare cellpopulation within whole blood;

FIG. 16A is a side view illustrating focusing for various densityparticles;

FIG. 16B is a graphical representation of data taken from FIG. 16Aillustrating the independence of particle density;

FIG. 16C is a side view of an inlet and an outlet of an exemplary systemillustrating the independence of particle density;

FIG. 17A is a graphical representation of the stability and precision ofinertially focused particles showing intensity profiles fitted to aGaussian;

FIG. 17B is a graphical representation of data taken from FIG. 17Ashowing FWHM and center position of focused particles versus time;

FIG. 18A is a side view of a channel of an exemplary focusing systemillustrating the self-ordering of particles;

FIG. 18B is a graphical representation of the data taken from FIG. 18A;

FIG. 18C is a side view of particle self-ordering within an asymmetriccurving channel of an exemplary focusing system;

FIG. 18D is a graphical representation of data taken from FIG. 18C;

FIG. 19A is a side view showing self-ordering for cells in diluted wholeblood within an exemplary focusing system;

FIG. 19B is a graphical representation of a segment of a peak plotobtained from the date of FIG. 19A illustrating the in-focus particles;

FIG. 19C is a graphical representation of a histogram of distancesbetween particles in the system of FIG. 19A;

FIG. 20A is a side view representing a spatial mapping of therotational, axial, and focal alignment of red blood cells is a channelof an exemplary focusing system;

FIG. 20B is a side view and cross-sectional view of rotational alignmentof discoid red blood cells within an exemplary focusing system;

FIG. 21 is a graphical representation of focusing results for a/D_(h)versus Dean number;

FIG. 22 is a side view of exemplary channels illustrating focusing forvarious a/D_(h);

FIG. 23A is a side view of channels for focusing various size particleswithin an exemplary focusing system;

FIG. 23B is a side view and representation of a random distribution ofparticles at an inlet and the separation of particles at an outlet usingan exemplary focusing system;

FIG. 23C is a top view of a tree configuration for a multi-channelexemplary focusing system;

FIG. 24 is a side view illustrating particle separation behavior forvarious R_(p) within an exemplary focusing system;

FIG. 25 includes top views of particle distribution at an inlet andparticle separations at an outlet for various particle sizes within anexemplary focusing system;

FIG. 26A is a graphical representation of particle diameterdistributions for an input solution and various output fractions withinan exemplary focusing system;

FIG. 26B is a graphical representation of one portion of the graphicalrepresentation of FIG. 26A illustrating the presence of largerparticles;

FIG. 27 illustrates purity and yield data for filtration of largeparticles from 3.1-μm particles;

FIG. 28 illustrates data for an exemplary focusing system havingcascaded separations with two tiers;

FIG. 29A is a representation of an exemplary focusing system forseparating various sized deformable silicone oil droplets;

FIG. 29B is a graphical representation of particle size distributionsfor the system of FIG. 29A;

FIG. 29C is a graphical representation of particle size distribution forrigid particles flown in the system of FIG. 29A;

FIG. 30 is a graphical representation illustrating a size cutoff for theseparation of platelets from other blood components;

FIG. 31 is a side view of an exemplary channel illustrating focusing insolutions having different total volume fractions;

FIG. 32A is a top view of the focusing of particles within an expandingspiral channel of an exemplary focusing system;

FIG. 32B is a side view of the longitudinal ordering of various particlesizes within the channel of FIG. 32A;

FIG. 33A is a representation of the lateral displacement of particleswithin an expanding spiral channel of an exemplary focusing system;

FIG. 33B is a further illustration of the lateral displacement ofparticles within the channel of FIG. 33A;

FIG. 33C is a graphical representation of the lateral displacement ofparticles for various a/D_(h);

FIG. 34A is a representation of focusing within an expanding spiralchannel of an exemplary focusing system for various R_(e);

FIG. 34B is a side view illustrating longitudinal ordering of variousparticle sizes within the channel of FIG. 34A;

FIG. 35A is a side view of relative particle size and ordering within anexpanding spiral channel of an exemplary focusing system;

FIG. 35B is an illustration of the focusing of 10-μm particles withinthe channel of FIG. 35A;

FIG. 35C is an illustration of the focusing of 10-μm particles withinthe channel of FIG. 35A;

FIG. 35D is a side view of a 10-μm particle within the channel of FIG.35A;

FIG. 35E is a side view of a 7-μm particle within the channel of FIG.35A;

FIG. 35F is a graphical representation of particle count versus particlesize within the channel of FIG. 35A;

FIG. 36 is a side view illustrating particle focusing behavior forvarious R_(e) within an exemplary focusing system;

FIG. 37 is a representation of focusing behavior in symmetric curvingchannels within an exemplary focusing system;

FIG. 38 is a top view of an exemplary channel representing thedependence of particle focusing on a/D_(h);

FIG. 39 is side view illustrating focusing behavior for exemplarychannels of various widths within an exemplary focusing system;

FIG. 40 is a side view illustrating focusing behavior for exemplarychannels of various widths within an exemplary focusing system;

FIG. 41 is a representation of focusing behavior for exemplary channelsof various widths within an exemplary focusing system;

FIG. 42 is a representation of focusing behavior for exemplary channelsof various widths within an exemplary focusing system;

FIG. 43 is a side view illustrating R_(e) dependent focusing forseparation within an exemplary focusing system;

FIG. 44 is a top view illustrating the focusing of blood cells within anexemplary focusing system;

FIG. 45A is a side view of streak images of cells focusing for variousR_(e); and

FIG. 45B is a representation of intensity cross-sections of culturedcells at various turns within an asymmetric channel.

DETAILED DESCRIPTION OF THE INVENTION

Certain exemplary embodiments will now be described to provide anoverall understanding of the principles of the structure, function,manufacture, and use of the devices and methods disclosed herein. One ormore examples of these embodiments are illustrated in the accompanyingdrawings. Those skilled in the art will understand that the devices andmethods specifically described herein and illustrated in theaccompanying drawings are non-limiting exemplary embodiments and thatthe scope of the present invention is defined solely by the claims. Thefeatures illustrated or described in connection with one exemplaryembodiment may be combined with the features of other embodiments. Suchmodifications and variations are intended to be included within thescope of the present invention.

The invention relates to the fields of microfluidics and analyteseparation. Various embodiments of the invention described below arebased upon the notion that laminar flow of a fluid through microfluidicchannels can result in the continuous and accurate self-ordering ofparticles suspended within the fluid. A variety of specific channelgeometries are illustrated that take advantage of this effect to createcontinuous streams of ordered particles constrained in three spatialdimensions. Particles order laterally within the x-y plane (orcross-sectional plane) of the channel and can also order longitudinallyalong the direction of flow. An additional dimension of rotationalordering can occur for asymmetrically shaped particles.

In general, the invention features methods and devices that separate andfocus streams of particles to equilibrium positions within a channelflow field based, at least in part, on inertial lift forces. Inrectangular channels, this can lead, for example, to four streams offocused particles spaced a distance apart from a center of each of thefour rectangular faces. For certain rectangular geometries, thisfour-fold symmetry can be reduced to a two-fold symmetry, with streamsof particles spaced apart from each of two opposed faces of the channel.

The invention can also include methods and structures that decrease thesymmetry of the system using a variety of forces, including, forexample, electromagnetic, magnetic, centrifugal, hydrodynamic, thermal,sonic, optical, and/or dielectrophoretic forces or combinations thereof.Although any force may be used to bias a particular potential minimumwithin the channel flow field, utilizing centrifugal forces with acurved channel structure has certain advantages. In this case, the forcewill increase with the square of the flow rate based only on a minorgeometric change with no additional mechanical or electrical partsrequired. For example, the symmetry may be reduced by using inertialforces inherent in the flow through an S-shaped rectangular channel toresult in a two-fold symmetry (down from four-fold) with a majority ofthe particles aligned with the flow in a periodic manner notcorresponding to the period of the underlying channel. The geometry ofthe channel may also be used to change symmetry either by changing theradius of curvature or the width of the channel in a periodic manner(the channels thus curving asymmetrically) to create a single focusedparticle stream.

Embodiments of the invention may be advantageous in that they may employa single stream input and require no moving parts or separate pressurecontrol. Embodiments of the invention can also provide methods that arelow cost and employ devices requiring simple, fault tolerant manufacturethat may also be miniaturized. Embodiments of the invention may beoperated continuously and at high volumetric flow rates with cascadingoutputs. The invention also requires no interactions with mechanicalfilters or obstacles and requires very low maintenance.

The principles relating to suspended particles are also applicable to avariety of biological materials, particularly to cells. The ability torapidly analyze and extract information from whole blood, for example,and its component cells is of great importance for medical diagnosticsand applications in basic science. Blood cells themselves contain anabundance of information relevant to disease, infection, malignancy, orallergy diagnosis. Systems and principles are presented herein relatedto inertial microfluidic technology as a solution for high-throughputand precise microscale control of cell and particle motion. Systems ofthe invention are ideally suited for applications in blood cell subtypeor rare cell enumeration, sorting, and analysis. Identification andanalysis of rare cells, in particular, requires large sample sizes andhigh-throughput. Rapid and simple microfluidic techniques presentedherein can surpass the limitations of conventional sorting techniquesthat limit the size of samples that can be analyzed. The ability tosort, order, enumerate, and analyze particles continuously,differentially, and at high rates in a simple channel will be broadlyapplicable in a range of applications in continuous bio-particleseparation, high-throughput cytometry, and large scale filtrationsystems.

While there are many configurations possible in a system for theself-ordering of particles within microfluidic channels, one embodimentof such a system 10 is illustrated in FIGS. 1A and 1B. As shown, thesystem 10 generally includes an inlet 12 that can be configured forintroducing a sample 24 having suspended particles 22 into the system. Amicrofabricated chip 14 can be provided and can have at least onemicrofluidic channel 16 formed therein for receiving the sample 24 andfor ordering and focusing the particles 22 suspended in the sample 24,as shown in FIG. 1B. A plurality of such channels 16 situated inparallel are formed in the exemplary chip 14 illustrated in FIG. 1A.

The plurality of channels 16 formed in the chip 14 can have numerousconfigurations which will be described in detail below. In general,however, the plurality of channels 16 can have a specified geometryconfigured to separate, order, and focus particles of a predeterminedsize suspended within the sample 24 such that one or more focusedstreams of particles 22 per channel 16 are provided at an output 26 ofthe chip 14. An analysis region 18 can be provided in proximity to theoutput 26 of the channels 16 to monitor, sort, count, image, orotherwise analyze the localized and focused streams of particles 22.

In one embodiment, chip 14 can be, or be part of, a particle enumeratingsystem. In particular, analysis region 18, in which the particles havebeen focused and ordered, could be subject to interrogation by adetector for the purpose of counting the particles. A variety ofdetectors are discussed below, as are systems for tagging particles fordetection, and these elements can also be used for enumeration.

As used herein, a “sample” must be capable of flowing through themicrofluidic channels of the system embodiments described. Thus, anysample consisting of a fluid suspension, or any sample that be put intothe form of a fluid suspension, that can be driven through microfluidicchannels can be used in the systems and methods described herein. Forexample, a sample can be obtained from an animal, water source, food,soil, air, etc. If a solid sample is obtained, such as a tissue sampleor soil sample, the solid sample can be liquefied or solubilized priorto subsequent introduction into the system. If a gas sample is obtained,it may be liquefied or solubilized as well. The sample may also includea liquid as the particle. For example, the sample may consist of bubblesof oil or other kinds of liquids as the particles suspended in anaqueous solution.

Any number of samples can be introduced into the system for particlefocusing and should not be limited to those samples described herein. Asample can generally include any suspensions, liquids, and/or fluidshaving at least one type of particle, cellular, droplet, or otherwise,disposed therein. Further, focusing can produce a flux of particlesenriched in a first particle based on size. In some embodiments, asample can be derived from an animal such as a mammal. In a preferredembodiment, the mammal can be a human. Exemplary fluid samples derivedfrom an animal can include, but are not limited to, whole blood, sweat,tears, ear flow, sputum, bone marrow suspension, lymph, urine, brainfluid, cerebrospinal fluid, saliva, mucous, vaginal fluid, ascites,milk, secretions of the respiratory, intestinal and genitourinarytracts, and amniotic fluid. In other embodiments, exemplary samples caninclude fluids that are introduced into a human body and then removedagain for analysis, including all forms of lavage such as antiseptic,bronchoalveolar, gastric, peritoneal, cervical, athroscopic, ductal,nasal, and ear lavages. Exemplary particles can include any particlescontained within the fluids noted herein and can be both rigid anddeformable. In particular, particles can include, but are not limitedto, cells, alive or fixed, such as adult red blood cells, fetal redblood cells, trophoblasts, fetal fibroblasts, white blood cells,epithelial cells, tumor cells, cancer cells, hematopoeitic stem cells,bacterial cells, mammalian cells, protists, plant cells, neutrophils, Tlymphocytes, CD4+, B lymphocytes, monocytes, eosinophils, naturalkillers, basophils, dendritic cells, circulating endothelial, antigenspecific T-cells, and fungal cells; beads; viruses; organelles;droplets; liposomes; nanoparticles; and/or molecular complexes. In someembodiments, one or more particles such as cells, may stick, group, orclump together within a sample. In such a configuration, a grouping orclumping of particles can be considered to be “a particle” for thepurposes of systems of the invention. More particularly, a grouping orclumping of particles may act and be treated as a single particle withinchannels of the invention described herein and can thus be sorted,ordered, separated, and focused in the same way as a single particle.

Non-biological samples can include, for example, any number of variousindustrial and commercial samples suitable for particle separating,ordering, and focusing. Exemplary industrial samples that can beintroduced into the system can include, but are not limited to,emulsions, two-phase chemical solutions (for example, solid-liquid,liquid-liquid, and gas-liquid chemical process samples), waste water,bioprocess particulates, and food industry samples such as juices,pulps, seeds, etc. Similarly, exemplary commercial samples can include,but are not limited to, bacteria/parasite contaminated water, water withparticulates such as coffee grounds and tea particles, cosmetics,lubricants, and pigments.

In some embodiments, a fluid sample obtained from an animal is directlyapplied to the system described herein, while in other embodiments, thesample is pretreated or processed prior to being delivered to a systemof the invention. For example, a fluid drawn from an animal can betreated with one or more reagents prior to delivery to the system or itcan be collected into a container that is preloaded with such a reagent.Exemplary reagents can include, but are not limited to, a stabilizingreagent, a preservative, a fixant, a lysing reagent, a diluent, ananti-apoptotic reagent, an anti-coagulation reagent, an anti-thromboticreagent, magnetic or electric property regulating reagents, a sizealtering reagent, a buffering reagent, an osmolality regulating reagent,a pH regulating reagent, and/or a cross-linking agent. Examples ofmethods for processing fluid samples for delivery to an analyticaldevice are described in U.S. Publication No. 2007/0196820 entitled,“System For Delivering a Diluted Solution” filed Mar. 3, 2004 andincorporated herein by reference in its entirety.

Particles suspended within a sample can have any size which allows themto be ordered and focused within the microfluidic channels describedherein. For example, particles can have a hydrodynamic size that is inthe range of about 40 microns to about 0.01 microns. More preferably,particles can have a hydrodynamic size that is in the range of about 20microns to about 0.1 microns. More preferably, particles can have ahydrodynamic size that is in the range of about 10 microns to about 1micron. It will be appreciated that particle size is only limited bychannel geometry, and particles both larger and smaller than theabove-described ranges can be ordered and focused within predeterminedchannel geometries having laminar flow conditions.

In another aspect of the system, a particle to volume ratio of thesample can optionally be manipulated or adjusted for conservation ofmass within the channels. In general, sorting, ordering, and focusing ofparticles is in-part dependent on interparticle spacing within channelsas well as the ratio of particle size to hydrodynamic size of thechannel. Various channel geometries described herein may require apredetermined particle to volume ratio of the particle to be focused inorder to achieve a required interparticle spacing and thereby maintainordering and focusing of that particle. In particular, the particle tovolume ratio of a particle suspended within a fluid can be calculatedand adjusted as needed to achieve focusing within certain channelgeometries. In general, a maximum particle to volume ratio for aspecified particle size and channel geometry can be determined using theformula:

${{MaxVolumeFraction} = \frac{2N\; \pi \; a^{2}}{3{hw}}},$

where N is the number of focusing positions in a channel, a is thefocused particle diameter, h is the channel height, and w is the channelwidth. Thus, samples can be diluted or concentrated to attain apredetermined ratio before and/or during introduction of the sample intothe system. Additionally, certain exemplary systems may require theratio to be adjusted after the sample is introduced into the channels.

Particle to volume ratios of a sample within the channels describedherein can have any value sufficient to enable ordering and focusing ofparticles. In general, the particle to volume ratio can be less thanabout 50%. In other embodiments, particle to volume ratios can be lessthan about 40%, 30%, 20%, 10%, 8%, or 6%. More particularly, in someembodiments, particle to volume ratios can be in a range of about 0.001%to about 5%, and can preferably be in a range of about 0.01% to about4%. More preferably the ratio can be in the range of about 0.1% to about3%, and most preferably in the range of about 0.5% to about 2%. As willbe appreciated by those skilled in the art, the particle to volume ratioof additional or extraneous particles within the sample, apart from theparticle to be focused, need not necessarily be considered or adjusted.As will be further appreciated by those skilled in the art, any numberof samples may not require any adjustment to the particle to volumeratio of the particle to be focused before, during, and/or afterintroduction into the system.

Various commonly used techniques for diluting or concentrating samplesfor adjusting a particle to volume ratio can be used in the embodimentsdisclosed herein. For example, a sample can be diluted or concentratedin batches before introduction into the system such that the sampleultimately introduced into the system has the required ratio beforebeing introduced through the inlet. In other embodiments, the system caninclude two or more inlets for introducing the sample simultaneouslywith a diluent or concentrate to effect dilution or concentration. Inthis way, the particle to volume ratio can be adjusted within thesystem, whether adjustment occurs within a chamber before the sample anddiluent or concentrate enter the channels or whether adjustment occursthrough mixing of the sample and the diluent or concentrate within thechannels. In another embodiment, the diluent or concentrate can beintroduced into a center portion, fork, or branch of a channel as may berequired by various applications after the unadjusted sample hastraveled within the channel for some distance. A person skilled in theart will appreciate the variations possible for adjusting the particleto volume ratio of a sample within the embodiments described herein.

Referring again to FIGS. 1A and 1B, one or more microfluidic channels 16can be formed in the microfabricated chip 14 and can be configured forreceiving the sample 24 via one or more inlets 12 in communication withthe channels 16. The channels 16 can be further configured for orderingand focusing particles of a predetermined size suspended within thesample into one or more localized streams or fluxes of particles 22 thatis directed into one or more outlets 26. In this way, particles in adilute solution can be concentrated as illustrated in the figure. Asillustrated in FIG. 1B, the localized flux 22 can include three or moreparticles 20 disposed longitudinally adjacent to one another and can beseparated by a substantially constant longitudinal distance. Particles20 within the flux 22 can also align rotationally relative to thechannel 16.

In general, “localization” refers to a reduction in the area of across-section of a channel through which a flux of particles passes. Insome preferred embodiments, particles can be localized within an areahaving a width of, at most, 1.05, 2, 3, 4, or 5 times the width of theparticles. Localization can occur at any location within the channel,but preferably occurs within an unobstructed portion of the channel. Forexample, localization can occur in a portion of the channel having lessthan 50%, 40%, 30%, 20%, 10%, 5%, 2%, 1%, or 0.1% reduction incross-sectional area. In certain embodiments, localization can occur ina channel having a substantially constant cross-sectional area.

Any number of microfluidic channels can be formed in the chip in anynumber of ways, described in detail below. In one exemplary embodiment,a single channel is formed on the chip for focusing particles therein.In other exemplary embodiments, a plurality of channels can be formed inthe chip in various configurations of networks for focusing particles.For example, 2, 4, 6, 8, 10, 12, and more channels can be formed in thechip. As shown in FIG. 1A, a tree configuration is particularlyconvenient for a multiple channel system. Any number of layers can alsobe included within a microfabricated chip of the system, each layerhaving multiple channels formed therein.

Various channel geometries can be included on a single chip. As shown inFIG. 1A, straight sections of channels are formed in the chip near theinlet for transporting and dividing flow lines as the sample isintroduced into the system. The straight sections of channel cantransition to any number of symmetric and/or asymmetric curved channelsfor focusing particles of a predetermined size as needed. As furthershown in FIG. 1A, the chip can also include straight sections ofchannels at an output region for analysis of focused particles,collection of focused particles, and/or for recombining stream lines. Aswill be appreciated by those skilled in the art, any number of curves orstraight sections can be included as needed within the chip. Additionalcurved sections of channels can serve as “off-ramps” for focusedparticle streams to facilitate additional separation based on labels ortags associated with the particles. Channel forks or splits can beincluded at any positions within the channels to further facilitatemanipulation of focused particles as needed for various applications.

Various channel dimensions can also be included within a single chip.Channel dimensions can decrease over the length of the chip tofacilitate filtering of the sample, or for other reasons specific to anapplication. Channel dimensions can be larger at the input area or atthe output area to enable forks or valve systems to be positioned withinthe channels, or to enable multiple stream lines to be separated anddirected to different locations for analysis or collection. In a similarway, cross-sections of various channels can also be changed as neededwithin a single chip to manipulate stream lines of focused particles forparticular applications. In general, any combination of channelgeometries, channel cross-sections, and channel dimensions can beincluded on a single chip as needed to sort, separate, order, and focusparticles of a predetermined size or particles of multiple predeterminedsizes.

The channels used in the systems described herein can have variousgeometries and cross-sections for focusing particles of a predeterminedsize suspended within a fluid. For example, in one embodimentillustrated in FIGS. 2A and 2B, a straight channel 30 is provided havinga rectangular cross-section with an aspect ratio of substantially 1to 1. As will be described in more detail below, particles of apredetermined size flowing within such a channel geometry will beseparated, ordered, and focused into four streamlines 32 a, 32 b, 32 c,32 d corresponding to four equilibrium points or potential minimums at adistance from each face of the four channel walls. In anotherembodiment, a straight channel 36 is provided having a rectangularcross-section with an aspect ratio of substantially 2 to 1. Particles ofa predetermined size flowing within such a channel geometry can beseparated, ordered, and focused into two focused streamlines 38 a, 38 bcorresponding to two equilibrium points or potential minimums along topand bottom walls across the width of the channel. In one embodiment, anaspect ratio of 1 to 2 can also be used.

The channels may also be curved as shown in FIGS. 3A and 3B. Forexample, symmetrically curved channels can be provided such as S-shaped,sinusoidal, or sigmoidal shaped channel 40 having a rectangularcross-section. Particles of a predetermined size flowing within such achannel geometry will be generally focused into two streamlines 42 a, 42b corresponding to two equilibrium points or potential minimums at adistance from left and right side faces of the channel. An aspect ratioof a sigmoidal channel 40 can be substantially 1 to 1 and/or can varyalong a length thereof. For example, the aspect ratio of a sigmoidalchannel can vary over the length of the channel between 1 to 1 and 2 to1 depending on the configuration chosen.

In another embodiment, asymmetrically curved channels are provided asshown in FIGS. 4A and 4B. While asymmetrically curved channels can havevarious shapes and configurations as needed for a particularapplication, in one embodiment an asymmetric channel 46 can generallyhave the shape of a wave having large and small turns, where a radius ofcurvature can change after each inflection point of the wave. Each largeand small turn can have a specified width of the channel associated withthe turn. In particular as shown in FIG. 4A, one-half of a wavelength ofthe wave can have a large curve with a radius R_(1a), R_(1b) defining awidth W₁. A second half of the wavelength can have a curve with a radiusR_(2a), R_(2b) defining a width W₂, where R_(1a) and R_(1b) can begreater than R_(2a) and R_(2b), and vice versa (and where R_(1a)=R_(2a)and R_(1b)=R_(2b) would be a sinusoidal, symmetric shaped channel asindicated above). In addition, W₁ can be greater than W₂, and viceversa. The wavelength having a first half with the radius R_(1a), R_(1b)and the second half with the radius R_(2a), R_(2b) can then be repeatedas many times as needed, varying after each inflection point, to providea specified length of channel with an asymmetric curve. Theasymmetrically curved channel 46 can also have a rectangularcross-section with an aspect ratio that can vary as needed over thechannel length depending on the nature of the asymmetry in the curves.In one embodiment, the aspect ratio can vary between 1 to 1 and 2 to 1.In this case, a single focused stream 48 of particles is createdcorresponding to a single equilibrium point or potential minimum withinthe channel 46. In other embodiments, asymmetric curving channels, inparticular an expanding spiral shaped channel 50 can be provided asshown in FIG. 4C, having a rectangular cross-section with an aspectratio of substantially 2 to 1, although the aspect ratio can vary. Inthis case, particles are focused into a single stream line a distanceaway from an inner wall of the channel corresponding to a singleequilibrium point or potential minimum within the channel.

Aspect ratios of all channels described above and herein, includingstraight, symmetric, and asymmetric, can vary as needed from oneapplication to another and/or as many times as needed over the course ofa channel. In embodiments illustrated in FIG. 4, aspect ratios are shownas 1 to 1 and 2 to 1, however, a person of ordinary skill will recognizethat a variety of aspect ratios could be employed. In addition, thechoice of width to height as the standard for determining the aspectratio is somewhat arbitrary in that the aspect ratio can be taken to bethe ratio of a first cross-sectional channel dimension to a secondcross-sectional channel dimension, and for rectangular channels thiswould be either width to height or height to width. By way of furtherexample, the aspect ratio of the channel of FIG. 4C could be expressedas either 2 to 1 or 1 to 2, as could the aspect ratio of the channelillustrated in FIG. 9A in which the height is twice the width.

Other channel cross-sections can also be included in each of thegeometries noted above. Channel cross-sections can include, but are notlimited to, circular, triangular, diamond, and hemispherical. Particlesof a predetermined size can be focused in each of these exemplarycross-sections, and the equilibrium positions will be dependent on thegeometry of the channel. For example, in a straight channel having acircular or hemispherical cross-section, an annulus or arc of focusedparticles can be formed within the channel. In a straight channel havinga triangular or diamond cross-section, particles can be focused intostreamlines corresponding to equilibrium positions at a distance fromthe flat faces of each wall in the geometry. As symmetric and asymmetriccurving channels are included having each of the exemplarycross-sections noted above, focusing streams and equilibrium positionscan generally correspond to that described above with respect to thechannels having a rectangular cross-section.

In general, there are certain parameters within straight, symmetric, andasymmetric microfluidic channels which lead to optimal ordering andfocusing conditions for particles suspended within a sample. Theseparameters can include, for example, channel geometries, particle sizewith respect to channel geometries, properties of fluid flow throughmicrofluidic channels, and forces associated with particles flowingwithin microfluidic channels under laminar flow conditions. It ispresently believed that the forces acting on the particles can bereferred to as inertial forces, however, it is possible that otherforces contribute to the focusing and ordering behaviors. Exemplaryinertial forces can include, but are not limited to, inertial lift downshear gradients and away from channel walls, Dean drag (viscous drag),pressure drag from Dean flow, and centrifugal forces acting onindividual particles. FIGS. 5A-7 will be used to illustrate conceptsassociated with these parameters in the theory described below, withFIGS. 5A-5B generally referring to parameters associated with straightchannels and FIGS. 6A-7 referring to parameters associated with curvingchannels. The theory discussed below is meant to be solely descriptiveand exemplary and, while the behavior of systems designed using theseprinciples can be predicted using this theory, the theory presentedshould not be considered as limiting the invention to any of theparameters associated with any of the system embodiments disclosedherein or any particular theory of operation.

In general, inertial lift forces in laminar microfluidic systems, suchas those described in the embodiments herein, can act to focus randomlydistributed particles continuously and at high rates into a singlestreamline. Particle geometry dependence can be used to develop systemsfor high-throughput separations. Channel geometry can be changed toreduce focusing particles from an annulus to four points, to two points,and then to a single point within the channel. Two additional levels ofparticle ordering can be observed, in particular, longitudinally alongthe channel length and rotationally (for asymmetric particles). Ingeneral, separation, ordering, and focusing is primarily controlled by aratio of particle size to channel size and the flow characteristics ofthe system. Advantageously, the focusing is independent of particledensity.

Lateral migration of particles in shear flow arises from the presence ofinertial lift, attributed mainly to the shear-gradient-induced inertia(lift in an unbounded parabolic flow) that is directed down the sheargradient toward the wall, and the wall induced inertia which pushesparticles away from the wall. Particles suspended in fluids aresubjected to drag and lift forces that scale independently with thefluid dynamic parameters of the system. Two dimensionless Reynoldsnumbers can be defined to describe the flow of particles in closedchannel systems: the channel Reynolds number (R_(c)), which describesthe unperturbed channel flow, and the particle Reynolds number (R_(p)),which includes parameters describing both the particle and the channelthrough which it is translating.

$R_{c} = \frac{U_{m}D_{h}}{v}$ and$R_{p} = {{R_{c}\frac{a^{2}}{D_{h}^{2}}} = \frac{U_{m}a^{2}}{vD}}$

Both dimensionless groups depend on the maximum channel velocity, U_(m),the kinematic viscosity of the fluid, and ν=μ/ρ(μ and ρ being thedynamic viscosity and density of the fluid, respectively), and D_(h),the hydraulic diameter, defined as 2wh/(w+h) (w and h being the widthand height of the channel). The particle Reynolds number has anadditional dependence on the particle diameter, a. The definition ofReynolds number based on the mean channel velocity can be related toR_(c) by R_(e)=2/3 R_(c).

Inertial lift forces dominate particle behavior when the particleReynolds number is of order 1. Typically, particle flow in microscalechannels is dominated by viscous interactions with R_(p)<<1. In thesesystems, particles are accelerated to the local fluid velocity becauseof viscous drag of the fluid over the particle surface. Dilutesuspensions of neutrally buoyant particles are not observed to migrateacross streamlines, resulting in the same distribution seen at theinlet, along the length, and at the outlet of a channel. As R_(p)increases, migration across streamlines occurs in macroscale systems. Ina cylindrical tube, particles were observed to migrate away from thetube center and walls to form a focused annulus. The theoretical basisfor this “tubular pinch” effect is a combination of inertial lift forcesacting on particles at high particle Reynolds numbers. The dominantforces on rigid particles are the “wall effect,” where an asymmetricwake of a particle near the wall leads to a lift force 60 away from thewall, and the shear-gradient-induced lift force 62 that is directed downthe shear gradient and toward the wall, as shown in FIGS. 5A and 5B. Arelation describing the magnitude of these lift forces (F_(z)) in aparabolic flow between two infinite plates is useful in understandinghow the intensity of inertial migration depends on system parameterswith the caveat that the derivation assumes R_(p)<1.

$F_{z} = {{\frac{\rho \; U_{m}^{2}a^{4}}{D_{h}^{2}}{f_{c}( {R_{c},x_{c}} )}} = {\frac{\mu^{2}}{\rho}R_{p}^{2}{f_{c}( {R_{c},x_{c}} )}}}$

Here f_(c)(R_(c), x_(c)) can be considered a lift coefficient and is afunction that is dependent on both the position of the particle withinthe cross-section of the channel x_(c) and the channel Reynolds number,but independent of particle geometry. At the equilibrium position, wherethe wall effect and shear-gradient lift balance, f_(c)=0.

Inertial lift acting on a particle leads to migration away from thechannel center. From the equation for F_(lift), an expression for theparticle migration velocity, U_(p), can be developed assuming Stokesdrag, F_(s)=3πμaU_(p), balances this lift force:

$U_{p} = {\frac{\rho \; U_{m}^{2}a^{3}}{3{\pi\mu}\; D_{h}^{2}}{f_{c}( {R_{c},x_{c}} )}}$

An estimate of the transverse migration velocity out from the channelcenter line can be made by using an average value off f_(c) ˜0.5 forflow through parallel plates. This calculation yields a value of 3.5cm/s for 10-μm particles in a flow with U_(m)=1.8 m/s. Traveling alateral distance of 40 μm requires traveling ˜2 mm downstream in themain flow. The previous equation for U_(p) also indicates that thelateral distance traveled will depend heavily on particle diameter,indicating the possibility of separations based on differentialmigration.

Channels with curvature create additional drag forces on particles. Whenintroducing curvature into rectangular channels, secondary flows developperpendicular to the streamwise direction due to the nonuniform inertiaof the fluid. In a parabolic velocity profile, one example of which isshown in FIG. 6A, faster moving fluid elements within the center of acurving channel can develop a larger inertia than elements near thechannel edges. These elements can move toward the channel outer edge,and in order to conserve mass at all points

$( {{{{\nabla{\bullet\rho}}\; \overset{->}{V}} + \frac{\partial\rho}{\partial t}} = 0} ),$

the fluid is recirculated along the top and bottom of the channel. Twodimensionless numbers can be written to characterize this flow, the Deannumber (D_(e)) based on the maximum velocity in the channel, and thecurvature ratio (δ). The Dean number, D_(e)=R_(c)(D_(h)/2r)^(1/2) andthe curvature ratio, δ=D_(h)/2r, where r is the average radius ofcurvature of the channel. For moderate D_(e)<75 observed in themicrofluidic systems described herein, the secondary rotational flow, orDean flow, consists of only two vortices. The velocity magnitude of theDean flow scales as U_(D) ρD_(e) ²/(μD_(h)) and therefore, Stokes dragon suspended particles due to this secondary flow becomes significantfor large D_(e). In particular, the Dean flow velocity dependence onDean number can be seen in FIG. 6B. FIG. 6B illustrates a simulation ofDean flow at an average streamwise velocity of 1 m/s, corresponding to aDean number of ˜10. The geometry in FIG. 6B is 50-μm in width at thesmaller turn and 80-μm at the larger turn. The main flow is coming outof the page. FIG. 6C is a graph further illustrating average secondaryflow (vortex) velocity magnitude as a function of changing Dean numberfor a single geometry. A quadratic relationship between D_(e) andaverage vortex velocity is observed for a constant geometry and agreeswith theory.

In general, the drag due to Dean flow, or Dean drag (F_(D)) scales as

${ F_{D} \sim\frac{\rho \; U_{m}^{2}{aD}_{h}^{2}}{r}}.$

Equilibrium separations can be conducted considering the balance ofthese two forces, Dean drag 64 and inertial lift 66, as shown in FIG. 7.In particular, FIG. 7 illustrates the cross-section of any asymmetriccurved channel depicting the superposition of the four stable positions68 a, 68 b, 68 c, 68 d due to inertial lift forces with the Dean flow. Apossible mechanism for biasing a single minimum is also presented. Thedominant viscous drag due to the Dean flow acts strongly at the channelmid-line, directing particles to one side of the channel over the other(for the opposite turn this force is of less magnitude in the oppositedirection, and does not surpass the inertial force). Once a particle 70is trapped in this minimum, it can remain because the viscous drag 64 atthe split point of the two vortices is less in magnitude than the sheargradient-induced lift 66. Particles at the top and bottom minimum maynot remain trapped because the viscous drag acts strongly here as well,and in the direction of a weaker shear gradient.

The ratio of lift to drag forces, R_(f) scales as R_(f)˜δ⁻¹(a/D_(h))³for a constant R_(c). Separations are ideal when R_(f)≥1 within thechannel cross section for a particle of a given size and less than 1 fora particle of another size. For R_(f), lift forces that push particlesto an equilibrium position dominate, while for R_(f)<1, dominant Deandrag overwhelms these equilibrium positions and leads to mixing ofparticles. The dependence on particle diameter cubed suggests effectiveseparation of particles with small size differences. The R_(f) relationalso suggests that the separation can be tuned to separate particlesover a range of diameters by modification of the geometry D_(h) andcurvature ratio (δ).

Theory predicts a limit to the speed of equilibrium separations.Previously, the dependence of the lift/drag ratio, R_(f) on R_(c) wasneglected. When this dependence is taken into account, velocities higherthan optimum are predicted to lead to defocusing. This is because theinertial lift force scales with the channel velocity squared (U_(m) ²)and the lift coefficient (f_(c)), where the lift coefficient decreaseswith increasing U_(m). Therefore, the inertial lift force increases at arate less than U_(m) ². This can be compared to the drag force due toDean flow which scales with U_(m) ². This leads to the ratio of theseforces, R_(f), decreasing with increasing U_(m) ².

Therefore, three flow regimes can be considered: (1) At low fluidvelocities, R_(f) may be larger than 1 over the majority of the channelcross section; however, the magnitudes of F_(z) and F_(D) are too low tocreate focused streams within the length of channel. (2) At intermediatefluid velocities, R_(f) may be greater or equal to 1 over a limitedregion of the channel cross section, and the magnitude of forces islarge enough to create focusing to one or more streams. (3) For highfluid velocities, R_(f) is less than 1 over the entire channel crosssection, and Dean drag is dominant, leading to particle mixing.

Using R_(f) one can predict the particle size cutoff below whichfocusing does not occur. R_(f) varies in magnitude across the channelcross section due to variation in F_(D) and F_(z) over this region. Thefunctional form of this variation, however, is not currently known andthus it is difficult to predict a priori a particle size cutoff for agiven geometry (i.e., for what particle size does R_(f) initially become<1 throughout the channel cross section). Thus, empirically determinedcutoffs can give unknown parameters in R_(f). The known geometry andcutoff can then be inserted into the equation R_(f)=1 to find thescaling of unknown positional dependent factors. This is because theparticle diameter below which the ratio, R_(f) first becomes less than 1over the entire channel cross section corresponds to the size cutoff inthat channel geometry. In other words, with decreasing particlediameter, R_(f) decreases to less than 1, resulting in particle mixingdue to Dean drag forces dominating.

A semi-empirical relationship is provided quantitatively as follows:First, the condition R_(f)(x_(c1))=k(ra_(c) ³/D_(h) ⁴)=1 is produced,where x_(c1) are the coordinates of the final position to become lessthan 1 within the channel cross section and k is a scaling factor. Theempirical parameters are the channel radius of curvature (r), the cutoffsize (a_(c)), and the channel hydraulic diameter. Solving for k for oneor more experimental systems allows the development of a relationshipthat can be applied to an unknown system and size cutoff:

${r_{2}\frac{a_{c\; 2}^{3}}{D_{h\; 2}^{4}}} = {r_{1}\frac{a_{c\; 1}^{3}}{D_{h\; 1}^{4}}}$

This treatment assumes that both systems are operated at a constantR_(c) and that particle sizes are small compared to the flow field,since x_(c1) is assumed to remain independent of particle size.

A simplified expression that dictates the geometry of a new channel toseparate at a new cutoff can then be developed. If the same radius ofcurvature is maintained, then an empirical relation for D_(h) as afunction of the cutoff diameter can be written as:

$D_{h\; 2} = {D_{h\; 1}( \frac{a_{c\; 2}}{a_{c\; 1}} )}^{3/4}$

If height is the dominant factor in determining the inertial lift forceand channels with large widths are considered, such that h is thedominant dimension for Dean flow, the equation for D_(h1) above can berewritten as h₂=h_(i)(a_(c2)/a_(c1))^(3/4). In general, particles closeto the center and outer wall will move toward the channel outer edge,and recirculate along the top and bottom of the channel until they reachan equilibrium position. In other words, the lift forces contribute tofocusing the particles in two positions, above and below the plane ofsymmetry of the channel, along the height while the dean forces affectthe lateral position. In accordance with R_(f), the lateral equilibriumposition can be manipulated simply by changing particle diameter (a),geometry (D_(h)), and curvature ratio (δ).

In accordance with the above-described theory, which is generallyapplicable to all channel geometries, various combinations of parameterswill result in localization of a flux of particles in a channel with agiven geometry. In general, in certain embodiments, the Reynolds numberof the flowing sample can be between about 1 and about 250, the Deannumber of the flowing sample can be less than about 20, and/or the ratioof particle diameter to hydraulic diameter can be less than about 0.5.Properties more particularly related to certain channel geometries inview of the above described theory will be discussed below.

As previously noted, FIGS. 2A and 2B illustrate one embodiment of astraight channel having a rectangular cross-section showing forcevectors acting on particles therein. Referring now to FIGS. 8A-8C, theseparation, ordering, and focusing of particles within these exemplarystraight channels will be discussed in more detail. In general, at lowflow rates, particles flowing within these exemplary channels distributeuniformly across the cross-section of the channel. As R_(p) is increasedwith increasing fluid velocity, patterns of particle segregation inlaminar flow become observable that depend significantly on channelscale and symmetry. In general, uniformly distributed particles inrectangular channels migrate across streamlines to four symmetricequilibrium positions 82 a, 82 b, 82 c, 82 d at the centers of the facesof the channel and toward the channel edge of a rectangular channel 80having an aspect ratio of 1:1, as shown in FIGS. 8A-8C. In theillustrated embodiment, particles 9 μm in diameter suspended in waterwere observed in 50 μm-wide square channels, providing a particlediameter to channel diameter of 0.18. An inlet region 84 is shown wherethe particles are initially uniformly distributed within the fluid butstart to focus shortly thereafter to the four channel faces, as shown inFIG. 8B. FIG. 8C illustrates that the degree of focusing increases withR_(p) at a given distance along the channel and also increases with thedistance traveled along the channel. For R_(p)=2.9 (R_(c)=90), completefocusing is observed after a distance of ˜1 cm.

In general, for a given particle size, focusing occurs at a specificdistance to the channel wall. The equilibrium position for particles is˜9 μm from the channel edge for R_(c)=90 and agrees with theoreticalpredictions of ˜8 μm in an infinite plane system (R_(c)=100). Thisdistance is also predicted to move closer to the wall for a givenparticle size as R_(c) increases. Focusing occurs at channel faces asopposed to corners despite the symmetric features of corners.Presumably, the dominant wall effect acts from two directions on aparticle within a corner, and creates an unstable equilibrium point, asshown in FIGS. 8A and 8B. Inertial lift forces alone allowtwo-dimensional focusing to four precise positions within the lateralface of a rectangular channel.

Referring now to FIGS. 9A-9D, an alternative rectangular geometry forstraight channels is provided. In one embodiment, the rectangularcross-section of a straight channel 90 can be adjusted to producedspecific and/or optimized focusing results. In particular, the aspectratio of the channel 90 cross-section can be changed from about 1 to 1to about 2 to 1 as shown in FIG. 9A. In addition, particle diameter tochannel diameter ratios greater than 0.3 can be employed. When theaspect ratio and the particle diameter to channel diameter are adjustedin this way, particle focusing and ordering can become much more robust(i.e. less deviation in position). In addition, ordering positionsreduce from four in the 1 to 1 rectangular channels described above totwo in the optimized channels, as shown in FIG. 9A, and particles in thetwo ordering sites 94 a, 94 b are observed to interact and order acrossthe channel 90. Ordering occurs for low to high particle concentrations,where only the particle-particle distance is affected by concentration.Importantly, particles become evenly spaced in the direction of floweven to high particle concentration (−50×10⁶/ml).

The new ordering provides a tighter distribution in particle lateralposition in the flow as well as improved particle-particle interactionsleading to long regular chains 92 of particles with uniform spacing inthe direction of flow, as shown in FIGS. 9B and 9C. Precision orderingof cells and particles of 5-15 μm in size can be demonstrated for avariety of particle/cell densities (<5%) at continuous flow, mostclearly illustrated in FIG. 9B. As noted above, the geometry changereduces the four ordering positions observed within square or 1 to 1ratio channels almost entirely to the two ordering positions 94 a, 94 b.Further, particles ordered in positions across the channel 90 alsointeract to create a uniform fluid buffer between them.

In one exemplary system having a 2:1 rectangular geometry, particles alltravel with a speed of 13.2-13.8 cm/s (mean fluid velocity being 11.9cm/s) and exhibit a center-center spacing of 42-45 μm between adjacentparticles when they are focused to the same side of the channel 90, butare separated by only 23-25 μm in the direction of flow when thealternating pattern is present. These two patterns can also be found incombination, the particular ratio of one to the other depending most onthe local concentration of particles; if the concentration is low, theparticle-particle spacing present within the linear array is allowed, asshown in FIG. 9C. As the local concentration increases, however,particles are found more frequently in the interstitial sites on theother side of the channel 90, as illustrated in FIG. 9B. Equilibriumparticle spacing at the end of a 6 cm channel is generally linearlydependent on the particle diameter and channel diameter.

In another embodiment shown in FIG. 9D, the conditions described withrespect to FIGS. 9A-C are applied to particles of two differentpredetermined types. The particles 92 of a first type (illustrated asopen circles) can be introduced into the channel through a first inputbranch (the lower branch in the figure as illustrated), while a secondparticle type (illustrated as closed circles) can be introduced into thechannel through a second separate channel branch, the upper input branchas shown in the figure. As shown, the two types of particles move fromseparate input branches into a single channel and are ordered andfocused into two streams corresponding to two equilibrium positions onopposite sides of the channel. Where the first and second particles arediffering cell types, particles having differing chemistries, or somecombination thereof, having the particles focused and ordered such thatthe particles generally alternate between particles of the first typeand particles of the second type as they travel down the channel allowsfor greater opportunities to observe and manipulate interactions betweenparticles of the first and second types.

While the illustrated geometry for achieving the effects described withrespect to FIG. 9 has an aspect ratio of 2 to 1, there is a range ofsubstantially non-1-to-1 aspect ratios for which these effects may beobserved. First, as noted above, the effects may be seen regardless ofwhether it is the width or the height that is twice the other dimension.Of course, the reduction in symmetry for rectangular channels forfocusing into two stream lines rather than four will occur so that twolonger sides will have focused stream lines of particles that arecentered along and spaced apart from the walls. In addition to ratios ofabout 1 to 2, this reduction in symmetry can be observed in rectangularchannels having dimensional ratios of approximately 15 to 50, 3 to 5,and 4 to 5. Accordingly, the effects can be seen for a dimensionalaspect ratio of approximately 0.3 (15/50) to a dimensional aspect ratioof approximately 0.8 (4/5), and that the effects can be seen regardlessof whether the longer dimension is the width or the height.

Curving channels having a sigmoidal shape are also provided, and aspreviously noted, FIGS. 3A and 3B illustrate one embodiment of such acurving channel. Referring now to FIGS. 10A-10C, the separation,ordering, and focusing of particles within these exemplary sigmoidalchannels will be discussed in more detail. Within curving channelsystems, symmetry can be reduced by additional inertial forces arisingfrom the particles and fluid. These forces can act in superposition withthe lift forces to change equilibrium positions of particles flowingwithin the fluid. The additional inertial forces generally act in theplus and minus y directions in microfluidic channels with a curvingsymmetric or sigmoidal geometry, as previously illustrated in FIG. 3B.This geometry can bias the two stable positions on the sides of achannel 100 and can reduce the number of particles collected at the topand bottom focusing points. When the force is sufficient to bias thedirection, only two lines of focused particles 102 a, 102 b occur, asshown in FIGS. 10A and 10B. As shown in FIG. 10B, particles are randomlydistributed in the channel 100 at an inlet 104. As R_(c) increasesbetween 0.5 and 5, focusing into two streams 102 a, 102 b can occur. AsR_(c) increases, mixed streams are again observed, in agreement with anincreased contribution from Dean drag.

An asymmetric curving geometry, such as that previously illustrated inFIG. 4A, can lead to a further reduction in symmetry of particlefocusing. Referring now to FIGS. 11A-11D, an exemplary channel 110having an asymmetric configuration will be discussed. In anasymmetrically shaped channel, the net force generally acts in onedirection, biasing a single stable position of the initial distribution,and creating a single focused stream of particles 112, as shown in FIGS.11A-11D. FIGS. 11A and 11B illustrate that a time-averagedunidirectional centrifugal and/or drag force favors focusing down to asingle stream between R_(e)=1-15. As shown, focusing becomes morecomplex as D_(e) increases. FIG. 11C further illustrates that particlesare focused to one position of minimum potential with the addition ofcentrifugal forces or drag forces in the −x direction. Complete focusingcan also occur for much smaller R_(p) ˜0.15 and for shorter traveleddistances (˜3 mm), as shown in FIG. 11D, than in the case of straightrectangular channels. This may partly be due to the mixing action of theDean flow allowing particles to sample the stable regions of the flowmore quickly. FIG. 11D also illustrates the state of the particles in arandom distribution near an inlet 114 of the asymmetrically curvedchannel 110, a second distribution near turn 7 of the channel, andfinally the tightly focused stream of particles 112 near the outlet ofthe channel.

Another exemplary asymmetric geometry can include an expanding spiralshaped geometry as previously shown in FIG. 4C. Referring now to FIGS.12 and 13, aspects of an exemplary spiral shaped channel 120 will now bediscussed. As described above, in a system with inertial lift alone,shear-induced lift forces pushing the particles towards the walls can bebalanced by the wall-induced inertia pushing particles away from thewall into an equilibrium position close to the walls. In one embodiment,two significant geometrical features result in equilibrium particlefocusing for high-aspect ratio geometry and curvature. For high-aspectratio geometry, the probability of finding a particle balanced by theinertial forces close to a roof 122 and bottom 124 along the channel 120width is always greater than close to the inner of outer walls. Thusparticles suspended within a sample will tend to focus towards twofocusing positions 126 a, 126 b, as shown in FIG. 12. The curvatureintroduces Dean drag that will push the particles in differenttransversal directions depending on position. As illustrated previouslyin FIG. 6A, the velocity field shown in arrows illustrates the magnitudeand direction of the effect to a particle. For example, a particlelocated in the center will be pushed towards the outer wall andrecirculated through the outer edge roof or bottom until the particlesreach the equilibrium position near the inner wall where the Dean forcesare superimposed to the inertial forces from the inner walls, as shownin FIG. 12. Hence, in one embodiment, the main forces impacting theparticle focusing in the channel height direction may be inertial liftforces, while the Dean forces have a strong influence on the lateralpositioning of particles. A particle can remain focused as long as theDean force trying to push the particle away from the inner wall isbalanced by the inertia lift force from the inner wall trying to pushthe particle towards the inner wall. This results in particles focusingin single-stream lateral positions in two parallel symmetric streamsalong the height of the channel. In addition to focusing, particles areordered in uniform spacing in the direction of the flow as shown in FIG.13. High-speed camera experiments reveal that the ordered particles flowin the same stream line 128, either in the bottom 124 or roof 122, or inalternating particle trains. The behavior seems to be random, and thespacing between the ordered alternating particle trains is alwaysshorter compared to the spacing in the same streamline for the particleconcentrations used.

Referring now to FIG. 14, any of the exemplary channels described abovecan be included in various system configurations as needed for anynumber of applications. In general, however, FIG. 14 illustrates oneembodiment of such a system 200 having a plurality of channels 202 forthe ordering and focusing of particles as described above. As shown, thesystem 200 can generally include an inlet 206 having one or more inletchannels 204 a, 204 b that can be configured for introducing a samplehaving particles suspended therein into the system 200 through a filtermechanism 208. A pumping mechanism 210 can also be included and can beassociated with the inlet 206 and/or with an outlet 212 for introducinga sample into the system 200 under positive or negative pressure.

A microfabricated chip 214 can be provided and can have any number andconfigurations of any of the channels described above formed therein.FIG. 14 illustrates a plurality of the channels 202 formed in themicrofabricated chip 214 that can be configured for receiving a sampleintroduced through the inlet 206 and filter 208. An analysis region 216can be provided in proximity to an output channels 218 of the channels202 to monitor, sort, count, image, or otherwise analyze the focusedstreams of particles. The output channels 218 can be provided to receiveand/or collect one or more focused streams of particles per channelafter the streams travel through the analytical region of the chip. Oneor more output channels 218 can also be provided for separatingparticles of a predetermined type away from a main stream of particlesvia a microfluidic valve. A controller 220, which can include any numberof hardware, software, and analytical elements can be included to assistin pre-sample processing, pumping, flow rate regulation, valveoperation, and any analysis to be performed on focused particles. Afterfocusing, particles can be collected from the output channels into areservoir or outlet 212 for initial or additional analysis elsewhere, orfor disposal.

Referring in more detail now to the system 200 described above, one ormore inlets can be provided for introducing samples and/or othersubstances into the channels within the system. An inlet can generallycontain an inlet channel, a well or reservoir, an opening, and any otherfeatures which facilitates the entry of particles into the system. Theopening in the inlet can be in a floor of the microfabricated chip, topermit entry of the sample into the device. The inlet can also contain aconnector adapted to receive a suitable piece of tubing, such as liquidchromatography or HPLC tubing, through which a sample can be suppliedfrom an external reservoir. The inlet is generally in fluidcommunication with the channels and is generally upstream therefrom. Asnoted above, a sample can be diluted or concentrated before entering thechannels and a separate inlet can be provided for introducing such adiluent or concentrate to mix with the sample to achieve a desiredparticle to volume ratio. Additional inlets can be provided for othersubstances having labels or tags as will be described below, tofacilitate mixing with the sample before introduction into the channels.Any number and combination of inlets can be provided. In the same way,any number of outlets can be provided for receiving and collecting thesample and focused streams of particles within the sample, as will bedescribed in more detail below.

Various methods can be used for identifying ordered and focusedparticles of a predetermined type within the channels. Labels or tagsfor identifying or manipulating particles to be focused within thechannels can be introduced into the sample before, during, and/or afterintroduction of the sample into the system. Labeling or tagging ofparticles is well known in the art for use, for example, influorescence-activated cell sorting (FACS) and magnetic-activated cellsorting (MACS), and any of the various methods of labeling can be usedin the systems described herein. In general, any techniques or methodsrelated to the identification and/or manipulation of particles based ontheir size, weight, density, electrical properties, magnetic properties,dielectric properties, deformable properties, fluorescent properties,surface characteristics, intraparticle characteristics such asinterparticle spacing, and/or rotational characteristics such asrotational rate, rotational frequency, and variation in rotational rateover a cycle, can be used, to name a few. In other embodiments,characteristics of a particle can be changed so that the particle can bemanipulated and/or identified based on its changed characteristic. Forexample, the size of a particle can be changed by adding a bead,particle, or other tag to it such that the particle will be shifted andfocused into a particular stream, and perhaps a particular channelbranch or outlet, based on its changed size. Exemplary labels caninclude, but are in no way limited to quantum dots, pentamers,antibodies, nano-beads, magnetic beads, molecules, antimers, affinitylabel beads, micro-beads, cell/cell signaling, etc. There is no limit tothe kind or number of particle characteristics that can be identified ormeasured using known labeling techniques, provided only that thecharacteristic or characteristics of interest be sufficientlyidentifiable. Exemplary labeling methods and techniques are discussed indetail in U.S. Pat. No. 6,540,896 entitled, “Microfabricated Cell Sorterfor Chemical and Biological Materials” filed May 21, 1999; U.S. Pat. No.5,968,820 entitled, “Method for Magnetically Separating Cells intoFractionated Flow Streams” filed Feb. 26, 1997; and U.S. Pat. No.6,767,706 entitled, “Integrated Active Flux Microfluidic Devices andMethods” filed Jun. 5, 2001; all of which are incorporated by referencein their entireties.

As noted above, particles can be labeled or tagged prior to introductionof the sample into the system. Alternatively or in addition, a secondaryinlet can be included in the system to facilitate introduction of labelsin parallel with introduction of the sample such that the labels andsample mix while entering the channels. In other embodiments, inletports can be included at various locations within the system alongchannel lengths such that mixing of labels and particles can occurwithin the channels before, during, and/or after focusing of theparticles.

Various techniques exist for moving the sample through the channelsdescribed herein and in general, the system can include a pumpingmechanism for introducing and moving the sample into and through thechannels. The pumping mechanism can also regulate and control a flowrate within the channels as needed. A specific pumping mechanism can beprovided in a positive pumping configuration, in a negative pumpingconfiguration, or in some combination of both. In one embodiment, asample can be introduced into the inlet and can be pulled into thesystem under negative pressure or vacuum using the negative pumpingconfiguration. A negative pumping configuration can allow for processingof a complete volume of sample, without leaving any sample within thechannels. Exemplary negative pumping mechanisms can include, but are notlimited to, syringe pumps, peristaltic pumps, aspirators, and/or vacuumpumps. In other embodiments, a positive pumping configuration can alsobe employed. A sample can be introduced into the inlet and can beinjected or pushed into the system under positive pressure. Exemplarypositive pumping mechanisms can include, but are not limited to, syringepumps, peristaltic pumps, pneumatic pumps, displacement pumps, and/or acolumn of fluid. Oscillations caused by some pumping mechanisms, such asa peristaltic pump, can optionally be damped to allow for properfocusing within the channels. Alternatively, the oscillations can beused to encourage mixing of particles and labels within the channels. Aswill be appreciated by those skilled in the art, any other pumpsconfigured for pumping fluid can be used depending on the requirementsof the system. A single pump can be used for all pumping requirements,including introduction of the sample, adjustment substances, and labels.Alternatively, independent pumping systems can be used to controlintroduction of independent samples, substances, and labels into thesystem. Generally, pumps can be interfaced with the system usinghermetic seals, such as silicone gaskets, although any mechanism ofinterfacing the pumps with the system can be used as needed depending onspecific configurations.

In another aspect of the system, flow rates within the channels can beregulated and controlled. This can include control of flow rate,impeding of flow, switching of flows between various input channels andoutput channels, and volumetric dosing. In an embodiment having aplurality of channels, the flow rate of samples can be controlled inunison or separately. In an embodiment in which the flow rate iscontrolled in unison, pressure supplied by the pumping mechanism can beadjusted as needed depending on the number of parallelizations ofchannels. Alternatively, variable and differential control of the flowrates in each channel can be achieved using various techniques known inthe art including, for example, a multi-channel individuallycontrollable syringe manifold. More particularly, the input channeldistribution can be modified to decouple all parallel networks ofchannels. An output can collect the output from all channels via asingle manifold connected to a suction. Alternatively or in addition,the output from each network can be collected separately for downstreamprocessing. Flow rate can be controlled by the pumping mechanism, avalve system, and/or by a controller.

Any number and variety of microfluidic valves can also be included inthe system to block or unblock the pressurized flow of particles throughthe channels. Valves can be positioned in or near any number of inletsand outlets, as well as in or near channels, channel branches, pumpingmechanisms, and controllers. In one embodiment, a thin cantilever can beincluded within a branch point of the channels such that it may bedisplaced towards one or the other wall of a main channel, typically byelectrostatic attraction, thus closing off or changing a pressureresistance within a selected branch channel. Alternatively or inaddition, valves can be microfabricated in the form of electrostaticallyoperated diaphragms, as are well known in the art. Mobile diaphragms andflexible membranes within a multi-layer structure can be used such thatunder pressure, flexing occurs to block or change resistance in or nearinlets, outlets, channels, and/or channel branches, and can redirectflows into specific channel branches and/or outlets. Typical processesfor including such microfabricated valves can include the use of, forexample, selectively etched sacrificial layers in a multi-layerstructure. In another embodiment, the microvalve can include one or moremobile diaphragms or flexible membranes formed in a layer above achannel branch, inlet, or outlet such that upon actuation, the membraneis expanded up to decrease resistance within a channel branch, inlet, oroutlet, or expanded down into the channel to increase resistance withinthe same. In this way, flow of particles within the channels can bedirected and controlled depending on predetermined parameters. Furtherdetails and discussion of such microfluidic diaphragms are disclosed inPCT Publication No. PCT/US2006/039441 entitled, “Devices and Methods forCell Manipulation” filed Oct. 5, 2007 and incorporated herein byreference in its entirety. A person skilled in the art will appreciatethat any microvalves and/or microfabricated valves known in the art canbe used within and throughout the system as required.

In another aspect of the system, one or more microfluidic, size-basedseparation modules or filters can optionally be included to preventclogging within the channels by preventing certain particle sizes orparticle types from entering the channels and/or to facilitatecollection of particles for downstream processing. Typically, particleslarger than the largest channel dimension can be removed prior toinjection into the channel to prevent clogging within the system. In oneembodiment, a filtering process can be performed apart from the systemto remove particles, including dust and debris, which are too largeand/or too small from the sample that will ultimately be introduced intothe channels. In another embodiment, one or more filters can be includedsomewhere within the system. For example, one or more filters can bepositioned just after the inlet such that the sample is required to passthrough the filters to enter the channels. One filter can be included toremove particles larger than a required size and another filter can beincluded to remove particles smaller than a required size. Filters canalso optionally be included within a positive pumping mechanism so thatthe sample is filtered before entering the inlet. Alternatively or inaddition, filters can be disposed within valve systems, within thechannels, and/or near the output of the channels as needed in specificconfigurations of the system. In other embodiments, channel sizes can besequentially reduced over a portion of the system to facilitateseparation of larger particles from the substance.

Various types of microfluidic filters known in the art can be used toremove specific particle sizes or types from the sample. Structuralfilters can be used for filtration, including mesh filters,microfabricated frits, pillar structures, microposts, affinity columns,or flow restrictions within channels. In one embodiment, one or moremesh-style filters can be used to separate specific particles from thesample. A mesh-style filter can mechanically prevent particles of acertain size from traveling through specifically sized holes or gapswithin the mesh. Additionally, the mesh can selectively allow passage ofparticles based on their size, shape, or deformability. Two or moremesh-style filters can be arranged in series or in parallel, forexample, to remove particles of increasing or decreasing sizesuccessively. In another embodiment, microposts, such as those describedin U.S. Publication No. 2007/0264675 entitled, “Microfluidic Device forCell Separation and Uses Thereof” filed May 8, 2007 and incorporatedherein by reference in its entirety, can be included in the outputregion of the chip. Microposts can be included in various positions onthe chip as needed for filtration. In one embodiment, if taggedparticles being analyzed and directed into a specified channel orreservoir are missed by another filter or analysis device, one or moremicroposts positioned downstream can act as a filter to direct theseparticles into an additional channel or collection reservoir to ensure alarger portion are collected. In other embodiments, diffusionalfiltration can be used in addition to or as an alternative tostructurally based filters.

A variety of techniques can be employed to fabricate the chip havingchannels formed therein for the separation, ordering, and focusing ofparticles. The technique used can be selected based, in part, on thematerial chosen for forming the chip. Exemplary materials forfabricating a microfluidic chip can include glass, silicon, steel,nickel, poly(methylmethacrylate) (PMMA), polycarbonate, polystyrene,polyethylene, polyolefins, silicones (for example,poly(dimethylsiloxane)), and any and all combinations thereof. Methodsfor forming channels within these materials are also well known in theart, and can include soft lithography, photolithography (for example,stereolithography or x-ray photolithography), molding, embossing,silicon micromachining, wet or dry chemical etching, milling, diamondcutting, Lithographie Galvanoformung and Abformung (LIGA), andelectroplating. For example, for glass, traditional silicon fabricationtechniques of photolithography followed by wet (KOH) or dry etching(reactive ion etching with fluorine or other reactive gas) can beemployed. Techniques such as laser micromachining can be adopted forplastic materials with high photon absorption efficiency. This techniqueis suitable for lower throughput fabrication because of the serialnature of the process.

For mass-produced plastic devices, thermoplastic injection molding, andcompression molding can be used. Conventional thermoplastic injectionmolding used for mass-fabrication of compact discs can also be used tofabricate the microfluidic chips described herein. For example, channelfeatures as well as other features required on the chip can bereplicated on a glass master by conventional photolithography. The glassmaster is electroformed to yield a tough, thermal shock resistant,thermally conductive, hard mold. This mold can serve as the mastertemplate for injection molding or compression molding the features intoa plastic device. Depending on the plastic material used to fabricatethe chip and the required throughput of the finished system, compressionmolding can be chosen as a preferred method of fabrication. Compressionmolding, also known as hot embossing or relief imprinting, has theadvantage of being compatible with high molecular weight polymers, whichare excellent for small structures. For high aspect ratio structures,injection molding can be a preferred method of fabrication but is mostsuitable for low molecular weight structures.

A microfluidic chip such as those described herein can be fabricated inone or more pieces that are then assembled. In one embodiment, separatelayers of the chip can contain channels for a single fluid. Layers ofthe chip can be bonded together by clamps, adhesives, heat, anodicbonding, or reactions between surface groups (wafer bonding).Alternatively, a chip having channels in more than one plane can befabricated as a single piece, for example using stereolithography orother three-dimensional fabrication technique.

In one particular embodiment, the chip can be formed of PMMA. Thefeatures, including channels, can be transferred onto an electroformedmold using standard photolithography followed by electroplating. Themold can be used to hot emboss the features into the PMMA at atemperature near its glass transition temperature (105° C.) underpressure (5 to 20 tons). The mold can then be cooled to enable removalof the PMMA chip. A second piece used to seal the chip, composed of asimilar or dissimilar material, can be bonded onto the first piece usingvacuum-assisted thermal bonding. The vacuum prevents formation of airgaps in the bonding regions. As will be appreciated by those skilled inthe art, the chip can be formed of any material or combination ofmaterials as needed for specific pressure requirements within thechannels, as well as specific channel geometries and size requirements.

As illustrated in FIG. 14 and as noted above, the system can optionallyinclude a controller. The controller can include, be operativelyconnected to, and/or control various analytical equipment or analyzersdisposed within the chip and/or around the chip to accommodateprocessing and analysis of focused particles as the particles enter theanalysis region, as well as to control various flow rates, pumpingsystems, and/or valve systems. An analyzer can include any sampleanalyzing device known in the art, such as, for example, a microscope, amicroarray, a cell counter, etc. An analyzer can further include one ormore computers, databases, memory systems, and system outputs, forexample, a computer screen or printer. In some embodiments, an analyzercan include a computer readable medium, for example, floppy diskettes,CD-ROMS, hard drives, flash memory, tape, or other digital storagemedium, with a program code having a set of instructions for detectionor analysis to be performed on the focused stream or streams ofparticles. In some embodiments, computer executable logic or programcode of an analyzer can be loaded into and/or executed by a computer, ortransmitted over some transmission medium, such as over electricalwiring or cabling, through fiber optics, or via electromagneticradiation. When implemented on a general purpose microprocessor, thecomputer executable logic configures the microprocessor to createspecific logic circuits. In one embodiment, the computer executablelogic performs some or all of the tasks described herein includingsample preparation, dilution, concentration, pumping, flow rateregulation, detection, and/or analysis. In some embodiments, thecontroller can be at a location remote from the chip, channels, pumpingmechanism, and other components of the system. For example, the chip,channels, and other system components can be located in one room,building, city, or location and the controller can be located in anotherroom, building, city, or location. The controller can be configured tocommunicate wirelessly with the components from a remote location toconfigure, control, program, and/or otherwise manage any and all aspectsof the procedures and devices related to the focusing of particles andanalysis of focused particles as described herein. The controller cancommunicate with the other components in a system of the invention usingany wireless technology known in the art, including but not limited to,Bluetooth, the IEEE 802.11 standard, Wi-Fi, broadband wireless, and/orany wireless communication that can be accomplished using radiofrequency communication, microwave communication, and infraredcommunication. The controller may utilize point-to-point communication,point-to-multipoint communication, broadcasting, cellular networks,and/or wireless networks. The controller may also utilize wired networkssuch as local area networks, wide area networks, and/or the Internet.

It is contemplated that the system described herein can be packagedtogether as a kit or singular unit for diagnostics and point-of-careapplications. In other embodiments, some, any, and/or all components canbe separate to work in individualized locations to maximize size and/orefficiency, for example in industrial applications. In one embodiment, akit or singular unit for diagnostics and point-of-care applications caninclude a microfabricated chip having channels formed thereon, a pumpingmechanism, valves, filters, controller, and any other components thatmay be required for a particular application. The components and channelconfigurations can vary as needed in a particular unit. In someembodiments, the unit can be in the form of an open system in whichvarious components of the system, for example, the chip, can be replacedas needed by a user. In other systems, the unit can be in the form of aclosed system in which no components can be replaced by the user. In anyof the embodiments and configurations, any and all components of thesystem can be single use, disposable, time limited, reconditionable,and/or reusable.

Any and all components of the system can be reconditioned for reuseafter at least one use. Reconditioning can include any combination ofthe steps of disassembly of the a system of the invention or systemcomponents, followed by cleaning and/or replacement of particularpieces, and subsequent reassembly. In particular, a system of theinvention can be disassembled, and any number of the particular piecesor parts of the device can be selectively replaced or removed in anycombination. Upon cleaning and/or replacement of particular parts, thedevice can be reassembled for subsequent use either at a reconditioningfacility, or by a surgical or research team immediately prior to aprocedure or test. Those skilled in the art will appreciate thatreconditioning of a device can utilize a variety of techniques fordisassembly, cleaning/replacement, and reassembly. Use of suchtechniques, and the resulting reconditioned device, are all within thescope of the present application.

The systems described herein can be used in a wide range of conventionalenumerating, sorting, concentrating and ordering techniques. There is anever increasing need in biological research, for example, for moreaccurate and efficient methods to manipulate and separate targetparticle and cell populations. Disciplines ranging from immunology andcancer medicine to stem cell biology are highly dependent on theidentification of uncontaminated populations of particular particle andcell subsets for detailed characterization. Clinically, microbiologistsroutinely isolate bacterial cells and white blood cell subsets fordiagnostic purposes. Tumor antigen-specific regulatory T cells can bediscovered in the circulating blood of cancer patients, presenting a newpotential target for immunotherapy of metastatic melanoma. Environmentalsensing requires surveillance of water, food and beverage processing forspecific bacterial cell contamination. Vaccine developers work largelywith antigen-specific T lymphocytes, rare cells which may differ fromone another by no more than a single amino acid in a peptide fragmentpresented on the cell surface. In these different applications a commonproblem is presented: the need to isolate, separate and characterizesubpopulations of cells present within heterogeneous, complex fluids.During the processing of these samples, the target cell population mustbe handled with gentle care, preventing alteration of the cell'sphysiological state to allow for subsequent expression profiling andmolecular studies. Moreover, the cells of interest may be present atextremely low frequencies-often less than 1 cell in 10,000,000 cells,for circulating tumor cells or disease-specific T lymphocytes,increasing the complexity of the challenge. As shown in FIG. 15C, thefrequency of the target cell population in whole blood, for example,varies greatly depending on the application, illustrating the necessityfor a dynamic sorting device that can process both small (10 μl) andlarge (10 ml) amounts of whole blood with equal specificity andefficiency without altering the integrity of the cells.

Applications for a sensitive, high throughput, point-of-care particleand blood cell manipulator are far reaching. In the area of prenataldiagnosis of genetic abnormalities, for example, fetal nucleated redblood cells are a promising candidate for non-invasive diagnosis.However, the concentration of nucleated red blood cells in maternalblood is very low (1 per 10⁶ cells), current cell sorting techniques arenot suitable for analysis. In the field of cancer research, the abilityto selectively isolate and characterize extremely rare (1 in 10⁹ cells)circulating tumor cells (CTCs) could transform patient diagnosis,prognosis and treatment. With increased throughput provided by systemsof the invention described herein, the potential exists to isolatecirculating tumor cells in very early stage cancer patients where thefrequency of cells is proposed to be even lower. Fundamental toself/non-self recognition, a T cell contains a unique surface receptorthat recognizes a specific peptide sequence, or antigen; although theexact diversity of T cells in the body is unknown, estimates suggestthat there are at least 2.5×10⁷ unique T cells in human blood. Isolatingthese cells becomes a significant challenge when their frequency inblood is quite low, thus requiring a large sample volume to be processedin order to isolate a statistically significant number of these cells.For example, in individuals latently infected with tuberculosis, thefrequency of CD8+ T cells specific for a particular T8 antigen may beless than 1 in 200,000 peripheral blood mononuclear cells, which is thelimit of sensitivity with existing sorting and ordering systems. Theability to measure even lower frequencies would be beneficial to vaccinedevelopment and diagnostics. Nonetheless, given 1 ml of whole blood,fewer than five specific antigen-specific T cells (ATGs) might bepresent, meaning that it might be necessary to process as much as 5-10ml of whole blood samples in order to obtain an ATG population of areasonable size, which conventional systems are incapable of doing inany time-sensitive manner, if at all.

The systems and methods described herein thus provide a manner in whichrare cells can be sorted, separated, enumerated, and analyzedcontinuously and at high rates. Whether a particular cell is a rare cellcan be viewed in at least two different ways. In a first manner ofcharacterizing a cell as rare, the rare cell can be said to be any cellthat does not naturally occur as a significant fraction of a givensample. For example, for human or mammalian blood, a rare cell may beany cell other than a subject's blood cell (such as a red blood cell anda white blood cell). In this view, cancer or other cells present in theblood would be considered rare cells. In addition, fetal cells(including fetal blood cells) present in a sample of the mother's bloodshould be considered rare cells. In a second manner of characterizing acell as rare might take into account the frequency with which that cellappears in a sample or with respect to other cells. For example, a rarecell may be a cell that appears at a frequency of approximately 1 to 50cells per ml of blood. Alternatively, rare cell frequency within a givenpopulation containing non-rare cells can include, but is not limited to,frequencies of less than about 1 cell in 100 cells; 1 cell in 1,000cells; 1 cell in 10,000 cells; 1 cell in 100,000 cells; 1 cell in1,000,000 cells; 1 cell in 10,000,000 cells; 1 cell in 100,000,000cells; or 1 cell in 1,000,000,000 cells.

Referring now to FIG. 15A, one embodiment of a particle sortingconfiguration for the systems described herein is provided. Inparticular, FIG. 15A illustrates a passive sorting mechanism in the formof a magnetic-activated particle sorting configuration 250. Amicrofabricated chip can generally be provided having one or moreasymmetric channels 252 formed therein. An analysis region of the chipcan also be provided in which an output region 254 of each main channel252 can include a fork or channel branch point that transitions the mainchannel 252 into first and second output channels 258, 256. A sample 260can be prepared for introduction into the system 250 and targetparticles 262 of a predetermined size can be directed into theasymmetrically curving channels 252 to be focused into a single, tightlylocalized stream.

Magnetic labels, tags, markers 264, or a reagent to render particles ofinterest magnetic, can be introduced into the system 250 and mixed withthe sample 260 before its introduction into the channels 252 and/orafter the particles 262 have been focused and before the particles 262enter the analysis region. As will be appreciated by those skilled inthe art, any and all conventional MACS methods and techniques can beused with the system 250 of the invention as noted above and as furtherdescribed in connection with the illustrated embodiment. For example,the particles 262 can be cells incubated with magnetic markers 264 inthe form of magnetic beads coated with antibodies against a particularsurface antigen of the cell. This causes the cells expressing thisantigen to attach to the magnetic beads. In other embodiments, certaincells, such as nucleated red blood cells, could be rendered magnetic byaltering the oxidation state of the cytoplasmic Hemoglobin with areducing agent. In addition, a cell can be sorted based on intrinsicmagnetic properties. Cells having internalized ferrous containingparticles, for example cells with saturated transferrin receptors, couldbe separated from other cells based on their higher magnetic moment. Instill another example, macrophages with ingested red blood cells can beseparated from other macrophages and white blood cells by virtue of themagnetic properties of the Hemoglobin in the ingested red blood cell.Regardless of the type of magnetic marker 264, the magnetic propertyused to identify a particle, or of where the magnetic markers 264 areintroduced, however, the markers 264 will ultimately be attached to thetarget particles 262 of a predetermined type within the focused streamof particles as they enter the analysis region.

As shown in FIG. 15A, the channels 252 can be configured such that thefocused stream of marked particles 262 and unmarked particles 266leaving the asymmetrically shaped portion of the channels 252 willnaturally flow into the second output channel 256. A magnetic biasingelement, such as a magnetic field gradient and/or a magnetic field 268,can be applied across the analysis region 254 near the channel branchpoint such that magnetically marked particles 262 will be deflected adistance away from the focused stream in response to the magnetic field268 and will enter the first channel output 258 instead of the secondchannel output 256. The tightly focused stream(s) of particles providedby any channel geometry, for example, straight, symmetric, and/or theasymmetric curvature of the channels 252 allows such a configuration asonly a relatively small amount of deflection by the magnetic field 268is required to direct the marked particles 262 into the first channeloutput 258. This allows systems of the invention to operate with lowernoise, better accuracy, and with higher throughput as the smallerdeflections required with focused particle streams allow for higher flowconditions. In one embodiment, separating cells with a weak magneticmoment is allowable because of the bare minimum deflection needed todeflect flow trajectory in a tightly focused stream. So directed, themarked and unmarked particles 262, 266 can be identified, sorted,counted, collected, and otherwise analyzed further as needed. A personskilled in the art will appreciate that any channel geometry can be usedin this configuration, and any number of channels and channel branchpoints can be included to separate particle streams and perform sortingin parallel configurations.

Particle stream precision is essential for magnetic sorting applicationsof the sort described above, as increased precision of initial particleposition leads to reduced false positives after magnetic deflection andincreased throughput. The lowest inertial force necessary can becalculated and used to produce single ordered streams of particles withvariation in center position <100 nm. Weaker inertial focusingequilibrium positions can facilitate magnetic deflection of labeledparticles. This value can be measured by analyzing images fromhigh-speed camera data and channel length can be adjusted as needed tocompensate for lower inertial forces. In one embodiment, a design thatinitially produces strong equilibrium focusing forces and then changesgradually to the smaller magnitude forces by increasing the channelwidth gradually can reduce the effective channel length.

FIG. 15B illustrates another embodiment of a particle sortingconfiguration for the systems described herein. In general, an activesorting mechanism is provided in the form of a fluorescence-activatedparticle sorting configuration 280. Similar to FIG. 15A, amicrofabricated chip can be provided having one or more asymmetricchannels 282 formed therein. The chip can include an analysis ordetection region 284 in proximity to an output region of each mainchannel 282. Each channel 282 can include a fork or channel branch pointthat transitions the main channel 282 into first and second outputchannels 288, 286.

A sample 290 can be prepared for introduction into the system 280 bytagging particles 292 of a predetermined type with an opticallysensitive tag that is detectable in response to a light source 294, asis done in conventional FACS systems. In general, a tag will associatewith a particle or with a characteristic of the particle, for examplewith a marker associated with the particle. The tag can be a dye,fluorescent, ultraviolet, or chemiluminescent agent, chromophore, and/orradio-label, any of which can be detected with or without a stimulatoryevent to enable fluorescence. In some embodiments, certain particles maybe naturally optically detectable without requiring a tag and in otherembodiments, a tagged particle may be optically detectable without theuse of a light source to stimulate a scatter response. The opticallysensitive tag can be prepared with the sample 290 before introductioninto the system 280, or the tag can be introduced some time after thesample 290 is introduced into the channels 282 and before the particles292 reach the detection region 284 of the chip. A person skilled in theart will appreciate that any and all conventional FACS methods andtechniques can be used with the system of the invention as noted aboveand as further described in connection with the illustrated embodiment.Once the sample 290 is introduced into the asymmetric channels 282,whether or not particles have been optically tagged, particles of apredetermined size can be focused into a single, localized and orderedstream of particles which will naturally flow into the second outputchannel 286 upon reaching the branch point.

An optical assembly 296 can be positioned in proximity to the detectionregion 284 of the chip and can generally include the light source 294,filters 298, optics 300, and a detector 302 positioned around thechannel output, a distance before the branch point, for detectingoptically sensitive tagged particles 292. The light source 294 canilluminate each individual particle in the stream of focused and orderedparticles as they pass through the detection region 284 of the channel280. As the particle is illuminated, the detector 302 can detect lightscattered by the particle 292 and/or the tag associated with theparticle 292, thereby identifying the particle as a predetermined type.Based on certain preset parameters, the detector 302 can communicate asignal to a controller 304 as to the type of particle passing throughthe detection region 284.

As a predetermined type of particle 292 passes through the detectionregion 284 and approaches the branch point, a controller 304 can, at theappropriate time, activate a change in a flow resistance associated withthe first and second output channels 288, 286 using, for example, any ofthe microfluidic valves of the type discussed above. In one embodiment,a valve membrane or diaphragm 306 can expand under positive pressureinto the second output channel 286 at the branch point, therebyincreasing the resistance against the sample flow to prevent a taggedparticle 292 from flowing into the second output channel 286. In thesame way and at the appropriate time, a valve membrane or diaphragm 308can expand under negative pressure out of or away from the first outputchannel 288 at the branch point, thereby decreasing the fluid resistancethrough the first output channel 288 and allowing the particle 292 toflow into the first output channel 288.

In another embodiment, the detection system can also include aFluorescence Polarization (FP) system. A change in polarization of aparticle tagged with a dye, over free dye, can enable gating and sortingof desired particles. Using FP, the tagged particles can further beseparated on size differences because tagged particles with differentsizes will exhibit different polarization values and can bedifferentially separated into individual outlets. A detector measuresthe FP value and signals the controller, which in turn changes thechannel resistance appropriately, as described above, to direct theparticles to an appropriate outlet.

As with the magnetic system of FIG. 15A, the fluorescence system of FIG.15B can provide significant advantages over conventional systems.Because of the sharp focusing of particles, only slight changes ofdirection are needed to determine the direction of a particularparticle, allowing for higher throughput with less noise. In addition,longitudinal ordering of particles significantly reduces noise as thesystem can more reliably distinguish the discrete positions ofindividual particles along the length of the channel and flow resistancechanges in output branches can be more easily time for accuracy. Sodivided, the tagged particles 292, as well as any untagged particles,can be identified, sorted, counted, collected, and otherwise analyzedfurther as needed. A person skilled in the art will appreciate that anychannel geometry can be used in this configuration, and any number ofchannels and channel branch points can be included to separate particlestreams and perform sorting in parallel configurations.

In other embodiments, existing particle enumeration systems, for exampleflow cytometry, FACS, and/or MACS, can include a system of the inventionto provide more accurate particle enumeration. A tightly focused streamof particles that is longitudinally ordered provides for extremeaccuracy in the counting of particles of a predetermined type. Particleswithin a focused stream are ordered such that each particle can pass apredetermined point within an analytical region of a chip individuallyto be counted and analyzed, eliminating error due to clumping ofparticles.

In one embodiment, a system of the invention can be used to concentrateparticles of a predetermined type from a dilute sample. Particles withina sample that are rare or dilute can be introduced into channels of thesystem having any geometry as noted above. The particles can be sortedand focused continuously and at high rates to achieve a concentratedsample in which the particles of a predetermined type are present withmuch higher frequency in a final sample in comparison to the originalsample. Branches from a single channel and/or from multiple channels ona chip can be included to remove small volumes of focused particles fromthe original, dilute sample flowing within the channel to a collectionreservoir containing the concentrated sample. A concentrated sample suchas this can provide easier analysis and manipulation of rare particlesand/or of particles that originate in a dilute sample.

Any number of system configurations can be provided for variousapplications, including sorting and counting as described above. Othersystem configurations can be designed to achieve certain specificresults and/or properties associated with particle focusing within thevarious channel geometries. In the examples below, certain propertiesassociated with the systems described herein will now be discussed inmore detail. While certain experimental conditions may be discussed inreference to certain properties or parameters, it is to be understoodthat the properties and parameters are widely applicable to any of thechannel geometries. Thus, a system of the invention can be configured invarious ways for identifying, sorting, counting, and to achieve anynumber of the properties and parameters discussed in the examples below.

Example 1

Ordering and focusing of particles in the various channel geometriesdescribed herein is unaffected by relative particle density, as will bediscussed in reference to FIGS. 16A-16C. When the density of thesuspending solution is changed so that the suspended particles areeither more or less dense than the solution (i.e., positive or negativebuoyancy) focusing can be unperturbed and can remain at a consistentlocation, as illustrated in FIGS. 16A and 16B. For example, whenparticles both less dense (silicone oil, ρ=0.95 g/ml) and more dense(polystyrene, ρ=1.05 g/ml) than the suspending fluid (ρ=1.00 g/ml), areloaded simultaneously, both will focus to the same position, as shown inFIG. 16C. The independence of particle density for particle focusing isnot consistent with a dominant centrifugal force acting directly onparticles and suggests that Dean drag F_(D) is the dominant effectleading to symmetry reduction.

In particular, as noted in detail above, effects present in curvingchannels include (i) an inertial (centrifugal) force on suspendedparticles (F_(cfg)=ΔmU_(p) ²/r) and (ii) secondary rotational flows dueto inertia of the fluid itself, Dean flow. For a constant geometry theaverage velocity of the Dean flow scales with the square of De. Two dragforces are considered that may act on suspended particles of radius, a,due to this secondary flow. Both viscous (Stokes) drag (F_(D)=6πμaU_(D))and pressure drag [F_(P)=(½)ρπU_(D) ²C_(d)a²)] may be significant.Velocity conditions necessary for single focused streams allowed anorder of magnitude calculation of the forces that may act in the system.For 10-μm particles in the range of channel velocities for successfulfocusing, F_(P) was <5% the magnitude of F_(D), indicating that viscousdrag (1-10 nN) is still more significant because of the small particlesizes. However, as the channel velocity increases, pressure drag mayplay a more dominant role because it increases with the fourth power ofD_(e), while viscous drag increases with only the square of D_(e). Thiscontribution may be significant for particle motion in higher velocityregimes, where focusing to multiple streams occurs. In the samesuccessful focusing regimes centrifugal forces on flowing particles arealso less in magnitude than those due to viscous drag (F_(cfg)˜0.1-0.4nN).

Based on this preliminary analysis that neglects particle wakes andinteractions with the flow field, it appears that the dominant forceresponsible for biasing particular stable positions is viscous drag dueto the Dean flow. Additionally, particles with density less and greaterthan the suspending fluid would experience centrifugal forces inopposite directions (Δm is of opposite sign) and not lead to focusing toa single stream. This further suggests that Dean flow-induced viscousdrag is the controlling force. An asymmetric channel may function asshown in FIG. 4. Here the viscous drag along the midline of the channelis larger, leading to directional bias, whereas particles already withinthe potential minimum, due to the superposed inertial lift forces,remain trapped. These particles cannot escape because of less viscousdrag on the particle in the region where the two vortices split orrejoin.

Example 2

Particles within the exemplary channel geometries described herein canbe ordered and focused with extreme precision and with stability, asshown in FIGS. 17A and 17B. In particular, the stability of the focusedstreams of particles over time is assayed to demonstrate the utility ofthe phenomenon for focusing in flow cytometer and coulter countersystems. The stability and precision of inertially focused streams canbe characterized by imaging a solution of 10-μm polystyrene particlesover 10 minutes of continuous flow at R_(p)=0.24. In the example shownin FIGS. 17A and 17B, each image had an exposure time of 700 ms,sampling an average of 1,100 passing particles. In FIG. 17A, intensityprofiles are obtained from each stream and a Gaussian fit is made tothis profile. There are two parameters involved: the center position ofthe Gaussian fit and the full width at half maximum extracted andplotted for each time point. In FIG. 17B, these two parameters areplotted for each point on the same axis. The average full width at halfmaximum of the focused stream was 5% larger than the average particlefull width at half maximum imaged on the same microscope system. Thestandard deviation of the center position of the focused stream wasdetermined to be 80 nm in the y direction, and the focused stream'saverage width was only 1.05 times the average width of a singleparticle. Although other external forces, such as magnetic, optical, anddielectrophoretic, can also be used to bias a particular equilibriumpositions within the rectangular flow field, an approach usinghydrodynamic forces with a curved channel structure may be ideal. Theadditional forces increase with the flow rate, and only a minorgeometric change is required to focus particles, with no additionalmechanical or electrical parts.

Example 3

FIGS. 18A-18D illustrate that in addition to the focusing of particlesacross the transverse plane of the channel, self-ordering of particlesin the longitudinal direction, along the flow lines can also occur.High-speed imaging (2-μs exposure) can be used to reveal characteristiclong trains of particles (10-15 particles) with uniform spacing thatalternate between the four stable lateral positions in rectangularchannels, as shown in FIGS. 18A and 18B, or are concentrated in a singlestream for asymmetric channels, as shown in FIGS. 18C and 18D. Inparticular, FIGS. 18A and 18C represent 10 μm diameter particles in aflow rate of R_(c)=120. As shown in FIG. 18A, trains of particles tendto alternate between positions instead of occupying severalcoincidently. FIGS. 18B and 18D represent autocorrelation functions(ACF) that confirm particle ordering with an average distance of 36 μmin the straight channel and an average distance of 48 μm in the curvedchannel.

As illustrated by the above embodiment, particle-particle distancesbelow a threshold are not favored, and self-ordering in a longitudinaldirection results. A shorter preferred distance is observed at higherR_(c) in rectangular channels than in asymmetric curved channels, asshown in FIGS. 18B and 18D. Ordered particle trains described herein arecomparable to macroscale systems, where it has been postulated thatpreferred distances may arise from the interaction of secondary flowsaround rotating particles in a shear flow. In this case, the detachedsecondary flow itself may act as an object. For example, rigid particles(˜0.5-mm diameter) in large (˜1-cm diameter) cylindrical tubes will formlong trains above R_(c) ˜450 with stable interparticle spacingdecreasing with R_(p). In the systems described herein, robust orderingoccurs for a lower R_(c) ˜90.

Example 4

In another embodiment, additional particle ordering and alignment can beobserved with reference to FIGS. 19A-20B. Self-ordering for cells indiluted (2% vol/vol) whole blood occurs as for particles in buffersolutions, as shown in FIG. 19A. Deformable particles such as cells mayexperience additional hydrodynamic forces in the applied flow field;however, from the experimental results whole blood, droplets, andcultured cells were found to behave as rigid particles in straight andcurving microchannels. FIG. 19B illustrates a segment of a peak plotobtained from the image by data convolution with a kernel representingthe in-focus particle. Intensity here represents the level of fit to anin-plane particle. Images at a rate of =15,000 cells per second wereobtained in this system. Using a time series extracted from consecutiveimages, the particles flowing through the detection volume can becounted and analyzed as shown in FIG. 19C. A histogram of distancesbetween particles is plotted demonstrating the limit on particle spacingthat allows easy analysis (5% of particles are spaced closer than 16 μmapart).

A fourth dimension of axial rotational alignment in asymmetric particlescan also occur within the channels described herein. FIG. 20Aillustrates a spatial map of red blood cells flowing through thedetector area over 20 ms. The rotational, axial, and focal alignment ofthe cells can be seen more clearly in magnification. Here, red bloodcells are aligned with the disc face In the plane of the image. Inparticular, discoid red blood cells aligned rotationally such that thedisk axis was parallel to the rectangular channel wall, as can be seenin most clearly in 20B.

Example 5

Referring now to FIGS. 21-22, various levels of focusing for cells andparticles of different sizes are provided as applications in separationstem directly from the differential focusing of particles of differentsizes. A range of particle diameters (2-17 μm) and channel sizes(D_(h)=10-87 μm) were tested over a range of R_(c)=0.075-225 for curvingasymmetric channels. The focusing results were plotted as a function ofD_(e) and the ratio a/D_(h), as shown in FIG. 21. In particular, asshown in the key above the plotted results of FIG. 21, no focusingcorresponds to filled squares, focusing to two streams corresponds toopen triangles, focusing to a single stream is represented by opencircles, and more complex behavior is shown as filled triangles. Datafor this graph was collected using various size particles (2-17 μm) aswell as 4 different channel geometries.

The results shown in FIG. 21 apply universally for any diameter ratioand Dean number falling within a specific region independent of thespecific geometry. For example a 2 μm particle in a 10 μm channel shouldfocus to the same extent as a 200 nm particle in a 1 μm channel. Inaddition, the lateral distance traveled in a straight rectangularchannel at constant R_(c) can theoretically be shown to increase witha/D_(h) cubed, yielding kinetic separations. In particular, FIG. 22illustrates the dependence of particle focusing on a/D_(h). Streakimages at the outlet are shown 3 cm downstream of the inlet for a flowat R_(e)=100. The image is shown at the recombination of two branches toillustrate the uniformity of the flow profile from channel to channel.Focusing becomes more diffuse as a/D_(h) decreases indicating ashallower potential well at the face in the y direction. This followsfrom the limiting case of an infinitely wide channel where no y force ispresent and focusing occurs only at the channel bottom and top. In fact,as the diameter ratio for particles in a square channel decreases, thechannel starts to show characteristics of a circular channel withfocusing in a modified annulus (note the high intensity at the edges fora/D_(h)=0.04). At a given distance focusing becomes more defined asR_(p) increases following the dependence of F_(z) on R_(p) ².

For an asymmetric system, the additional effects due to Dean flow actalong with inertial lift to shape the allowable range of particles andchannel dimensions for successful focusing of particles into singlestreams. From the experimental data and theoretical calculations a largeregion for successful particle focusing can be defined wherea/D_(h)>0.07. Below this value two effects scaling with a/D_(h) mayresult in a loss of focusing: (i) inertial migration (scaling with(a/D_(h))³ is slower than what is required for complete focusing in thegiven length of the channel); or (ii) Dean drag becomes much larger thaninertial lift for all values of R_(c) as a/D_(h) becomes small. Anotherlimit is seen for D_(e)>20; above this level, drag from Dean vortices islarger than the inertial lift forces for most particle sizes and leadsto particle mixing. Still, sufficient Dean flow is necessary to biasparticular equilibrium points (a line of constant average Dean drag isdrawn with the value F_(D)=0.5 nN). Last, a practical limit is seen fora/D_(h)=0.5, where particle obstruction of the channels may occur.

The data plotted in FIG. 21 appear similar to a phase diagram and arecritical for determining the correct design conditions. In particular, avertical movement on the diagram corresponds to changing particle sizeif channel geometries are held constant. To effect a separation, onemust choose a region in the phase diagram (i.e., a specific geometry)where a small change in particle size leads to a change from a focusedto an unfocused stream. Thus, one particle size is focused to aparticular streamline and can be collected as an enriched fraction,whereas the other, smaller, particles are unfocused.

Example 6

In other embodiments, high-throughput separations are possible withthese systems because of the high R_(c) at which they operate, anexample of which is shown in FIGS. 23A-23C. For a flow rate of 1.5ml·min⁻¹ of 1% particle solution a mass sorting rate of ˜1 g·hr⁻¹ can beachieved for an unoptimized device that covers an area of 1.6 cm².Particles close in size (4 and 7 μm) can also be separated by tuning theasymmetric channel geometry, as shown in FIG. 23A, although withslightly less throughput. In these systems there are no externallyapplied forces other than the pressure to drive the flow, and thereforeit is straightforward to cascade and parallelize these design elements,as shown in FIG. 23C, to enhance enrichment and throughputs to very highlevels, or combine elements with different hydraulic diameters toseparate across more than one size threshold. Ideally pure fractions canbe collected through the use of multiple outlets as shown in FIG. 23A inwhich streak images show at the left, focusing is shown in the middleframe, and four collection channels are shown at the outletdemonstrating the feasibility of the separation in a channel 1 and 3.FIG. 23B further illustrates such a separation. The inlet is shownhaving a random distribution of particles therein. One type of particlecan be focused and separated out from the rest of the sample and threedifferent outlets 1, 2, and 3 can be provided as shown. The focusedparticles can be directed into outlet 1 and collected in a reservoir asshown, while the rest of the sample is collected in outlets 2 and 3.Typical of most microfluidic systems, a throughput of 30 mg·hr⁻¹ wasdescribed for deterministic displacement with a device area of 15 cm².In applications dealing with rare cell cytometry and purification orindustrial filtration, however, increased throughput is essential.

Example 7

Referring to FIG. 24, rapid (1 mL/min) separation and filtration ofrigid particles, emulsions, and blood components is also provided. Inone embodiment, flow conditions in the system were tuned to achieve thebest particle focusing with the highest possible flow rates. Streakimages of 10 μm fluorescent beads are shown at various controlled flowrates in the system described herein. As shown in FIG. 24, for lowchannel Reynold's numbers, particles are seen to be distributed randomlythroughout the channel width. As R_(p) increases, there is a gradualchange to one focused streakline near the outer edge of the larger widthchannel. For R_(p) larger than ˜2, the particle stream again becomesmore diffuse. It is also observed that the position of the focusedstreakline moves out from the wall of the larger turn with increasingparticle Reynold's number. Using this data, an optimal flow rate of, forexample, 0.9 mL/min (R_(p)=1.53) can be used to operate the systemsdescribed herein for exemplary separation applications.

Example 8

Referring now to FIGS. 25-27, a flow rate of 0.9 mL/min, 20 mL of amixture of 9.0- and 3.1-μm diameter polystyrene beads can be introducedinto the system. As shown in FIG. 25, fluorescent streak images revealessentially uniformly distributed particle positions at the input forboth particle sizes. At the outlet of the device, 9.0-μm-diameterparticles can be observed in a focused streakline, while 3.1 μmparticles remained unfocused. In one embodiment, five fractions werecollected from the system and were labeled according to the scheme inFIG. 25. Particle diameter distributions were obtained by CoulterCounter for the input solution and various outlet fractions, adistribution of which is shown in FIG. 26A. The size distribution for3.1 μm particles was narrow and contained a few extra peaks at 3.6 and4.2 that correspond to two and three aggregated particles. For alloutput fractions, there were significant levels of 3.1 μm particles;however, the significant majority of the distribution of particlescentered on 9-μm were collected from fraction 5.

Fraction 4 also contained some larger particles, as shown in FIG. 26B,where interestingly, the collected particles had a lower mean centeredon 8-μm with a distribution that was 20% narrower than the initialdistribution of large particles. The mean and standard deviation of thecollected particles were determined by fitting the counts to a Gaussiandistribution. The purity and yield for filtration of large particlesfrom 3.1-μm particles is shown in FIG. 27, where percentages refer toabsolute particle numbers. Purity is defined as the percentage of totalparticles in a fraction of the filtrate that were 3.1-μm in diameter,and yield is the percentage of total 3.1-μm particles recovered. Asshown in FIG. 27, there are definite trade-offs between yield andpurity, which can be useful for deciding collection strategies forparticular applications.

Example 9

Another embodiment of the system can be described with reference to FIG.28. Because large quantities of particles can be filtered in relativelyshort periods of time, separations like that shown in FIG. 25 can beeasily cascaded in series to reach higher levels of enrichment iffiltrate from the five outlets is merged into two pools. FIG. 28presents data for a cascaded separation with two tiers. In oneembodiment, filtration from fractions 1-4 were pooled and run throughthe system again, and the same was done with fraction 5. Key parametersthat are reported at each tier are the absolute numbers of particles,the ratio between 3.1- and 9-μm particles (ratio 3/9) and the enrichmentratio (i.e., the tier X 3/9 ratio divided by tier 0 3/9 ratio). Thissample consisted of pooling fractions 1-4 of the first pass, runningthis through the system, and collecting fractions 1-4 again. Notably,after two tiers of separation, ˜56% of the initial 3.1-μm particles werecollected in a sample, where the number of 9-μm particles was reduced by3 orders of magnitude (i.e., 99.9% purification).

Example 10

In this example, the behavior of deformable particles is illustrated. Inparticular, droplets of a fluid that is generally immiscible in solutionare shown to behave much like other particles in their focusing behaviorin channels. In embodiments shown in FIGS. 29A-29C, various sizedsilicone oil droplets that are not rigid can also be separated using thesystem described herein. A continuous distribution of silicone oildroplets (ρ=0.95 g/cm³, μ=10 cst) (ranging in size from <1 to 20-μm) canbe introduced into the system at a flow rate of 0.9 mL/min, as shown inFIG. 29A. In particular, as shown, the input solution of droplets iswell mixed. After passing through the separation channel, largerdroplets are seen to focus while smaller droplets remain unfocused. Thefive collected fractions showed obvious differences in content of largedroplets by phase contrast microscopy that corresponded with the videoresults of focusing streamlines shown in FIG. 29A. The fractions alsoshowed particle size distributions, represented in FIG. 29B, that agreedwell with the microscopy data. The continuous droplet size distributionsfor the collected fractions clearly show a size cutoff for separationwith the exemplary geometry (3.7-μm by fitting the data from fraction 3with a Boltzmann sigmoidal function to accurately determine the positionof 50% depletion).

Following the distribution shown FIG. 29B, one can estimate that equalnumbers of 4.5-μm particles could be filtered from 3-μm particles with aseparation purity of >90% with 50% of the 3-μm particles beingrecovered. Interestingly, size cutoffs for rigid particles are similarto that of deformable particles. For example, rigid PDMS beads with adifferent distribution ranging from <2 to 40-μm were fractionated usingthe same system and flow settings, as shown in FIG. 29C. In this case,the size cutoff of fraction 3 was determined to be 4.0-μm slightlyhigher than for deformable particles. Another noticeable difference isthe larger concentration of smaller particles in fraction 5 and thereduction in larger particles in fractions 1-3. Overall, the separationbehavior for rigid and deformable particles appears remarkably similar,with the bulk of large particles collected in fraction 5 and to a lesserextent 4. In both cases, fraction 2 has the lowest concentration ofparticles over the entire size range.

Example 11

The size cutoff for an the exemplary system described above is usefulfor separation of platelets (2-4 μm) from other blood components, asillustrated in reference to FIG. 30. In one embodiment, the separationof platelets from blood cells in diluted blood (2% whole blood in PBS)can be examined using a same flow rate of 0.9 mL/min. The cellularcomponents of blood range in size from 7 to 15-μm for sphericalleukocytes (WBCs), to 6-8-μm×2-μm for discoid RBCs, while platelets arebetween 2 and 4-μm in diameter. One microliter of blood contains ˜5×10⁶RBCs, (2-5)× 10 ⁵ platelets, and (5-10)×10³ WBCs². The original bloodsolution diluted to 2% was examined by flow cytometry, as shown in FIG.30. The initial number ratio of platelets to other cellular componentsin blood was 0.04. After passing 10 mL of diluted blood (200-μL wholeblood) through the system and collecting the five various fractions,enrichment or depletion of the platelet population was observed. Infraction 5, the amount of platelets was depleted compared to largercells by a factor of 2, while in fraction 3 the relative amount ofplatelets was enriched by a factor of 100.

Example 12

The experimental data suggesting an optimal flow rate for focusing agreewith theoretical predictions, despite theoretical assumptions of smallR_(p). At a low maximum channel velocity (U_(m)), lift is dominant;however, there is not enough distance in the channel for particles toreach equilibrium positions, as previously illustrated in FIG. 24 in thechannel having the low particle Reynolds number R_(p). As U_(m)increases, the ratio of lift to drag forces (R_(D) approaches 1; here asingle equilibrium position is favored due to the superposition of Deandrag and inertial lift forces, shown in the two channels having middleReynolds numbers R_(p) in FIG. 24. As U_(m) increases further, R_(f)becomes less than 1 over the channel cross section and focusing isperturbed by Dean drag, as illustrated by the channel with a high R_(p)in FIG. 24. These results suggest that theory for finite R_(p) shouldhave a dependence on increasing flow velocity similar to the small R_(p)theory used.

Using the experimental data determining size cutoffs for focusing, asemi-empirical relationship to predict future geometries that wouldfocus at given size cutoffs can be developed. For the particularconditions described herein, R_(f) ˜1 for a particle diameter of 4.0-μm,a hydraulic diameter of 90-μm and R_(c)=115. To determine a new geometryfor a size cutoff a_(c), the experimental parameters can be substitutedinto the following equation:

${r_{2}\frac{a_{c\; 2}^{3}}{D_{h\; 2}^{4}}} = {3.2 \times 10^{- 4}}$

Assuming that the radius of curvature is left constant in a new system,the new hydraulic diameter is a function of the desired cutoff:

D _(h2) =a _(c) ^(3/4) m ^(1/4)

This relation suggests that, for a cutoff of 8-μm, a D_(h) of 150-μm isrequired for a channel height of ˜95-μm if the width remains constant.This value can be acquired for the scaling of the balance of forcesbased on a single geometry; determining whether the value converges forseparate geometries would provide further support for this approach.Overall, the semi-empirical approach provides the scaling for the ratioof lift to drag forces without providing the magnitude of the individualforces. The speed of focusing, based on the magnitude of lift forces,can be calculated from the fundamental equations.

Blood cells may be considered to fail on the continuum between rigidparticles and deformable droplets; however, since droplets are measuredto have a size cutoff similar to rigid particles (3.7 vs. 4.0-μm) theequations presented above are also applicable to cells. The lack of adisparity between deformable droplets and rigid particles suggestssimilar ratios of inertial lift to Dean drag forces with littleadditional contributions. The differences, including the relativereduction of smaller particles in fraction 5 of the sorted droplets andthe reduced collection range in fraction 4, may be due to forces thatare known to act on flexible particles due to deformation in the flownamely, deformation-induced lift forces that additionally act to pushdeformable particles toward the channel center. These differences,however, should be small in the inertial flows since inertial liftforces have been shown to dominate droplet behavior for small drops orwhen the viscosity ratio between droplet and suspending fluid is 1 orgreater. For highly viscous droplets or cells, the droplet can beexpected to behave almost as a rigid particle.

Example 13

Referring to FIG. 31, inter-particle interactions can play a role inseparations, leading to varied behavior for solutions with differenttotal volume fractions. Because the system focuses particles toparticular streamlines, one upper limit of particle concentration of ˜5%can be calculated, in which all particles are in contact and aligned ina single file. However, even below this concentration, particle-particleeffects can limit the degree of focusing. Particles randomly disturb theideal parabolic flow of the fluid necessary for precise values ofinertial lift and Dean drag, as can be seen in FIG. 31. In particular,FIG. 31 illustrated particle concentration effects on ordering.Fluorescent streak images are shown for increasingly concentratedsolutions of 9-μm beads flowing through 50-μm focusing channels. Idealfocusing to a single stream is seen at 0.1% volume fraction ofpolystyrene beads. Focusing at 1% also remains relatively unperturbed.As concentrations increase further, the focusing is perturbed to agreater extent. A maximum concentration for which focusing could bepossible into a single-file stream is ˜4% for this geometry, but thiscalculation assumes particles are touching, and is not physical. Belowthis concentration focusing is still disturbed because beads change theideal flow pattern in their vicinity as they traverse the channel.

Example 14

Referring back to FIG. 23C as well as to FIG. 30, cell viability can bemaintained during inertial focusing. Because cells travel at highvelocities (˜0.5 m/s), it is important to evaluate cell viability anddamage during this process. It should be noted that cells traveling atsteady state with the fluid experience only small normal and shearstresses over their surfaces, while significant forces are briefly feltin the inlet and outlet regions where cells must be accelerated by thefluid. In the systems described herein, the channel width at the inletcan optionally be gradually tapered to minimize this effect. High cellviability is found by vital stain after passing through an exemplarysystem. Further evidence of little damage is seen in FIG. 30, wherescatter plot width and position for blood before processing appearsessentially unchanged after passing through the system. Cell debris andblebbing would produce a broader distribution of scatter.

No significant alterations in cell viability occur after they are passedthrough the inertial focusing systems described herein at high speeds.Even at average velocities of 0.5 m/s there was no discernable damage tocells (99.0% vs. 99.8% initial viability as measured by using afluorescent live/dead assay). High cell viability and throughput arecritical for applications such as flow cytometry. With inertialself-ordering, clear advantages emerge compared with hydrodynamicfocusing used in current flow cytometers. These include (i) a singlestream input, (ii) reduction of multiple cells in the interrogation spotbecause of longitudinal self-ordering, and (iii) angular orientation ofnonspherical particles for uniform scatter profiles. Another powerfuladvantage of this focusing system is that throughput can be easilyscaled by parallel channels, as noted above and as shown in FIG. 23C,because additional fluidic channels for the sheath fluid are notrequired. FIG. 23C demonstrates parallelization of particle alignmentfor high-throughput analysis. Sixteen parallel channels can be fed froman initially randomly distributed solution of 10-μm particles. Auniformly distributed input can be focused into 16 stable streams at theoutlet.

Example 15

The relative separation performance of the system can also be consideredherein. In particular, it is important to characterize the relativeperformance of the separation embodiments disclosed herein bydetermining several key figures of merit, which are applicable indifferent situations. In most cases it is difficult to compare betweenvarious techniques, since usually only a single figure of merit thatbest suits the application is reported. Here four quantifiable measuresof performance for separation systems are proposed that would allow easycomparison from device to device: (1) throughput, (2) enrichment ratio,(3) yield, and (4) separation resolution. As trade-offs between thevarious measures are possible by changing the conditions of separation,these parameters should be reported together for each reportedcondition. The throughput of the system is defined as the amount ofvolume sorted in a given time period. The throughput (Q_(m)) can begiven by Q_(m)=Q_(Φ), where Q is the volumetric flow rate, and Φ is thevolume fraction of particles input. Additionally, for most systemsincreasing the device footprint (i.e. parallelization) increases thedevice throughput linearly. Therefore the throughput per unit area (mLhr⁻¹ cm⁻²) is a useful measure. In one exemplary system, a throughput of0.6 mL hr⁻¹ was achieved with a device area of 2.5 cm². Enrichment ratiois defined as the number of selected particles to unselected particlesin the filtrate divided by the initial fraction of selected/unselectedparticles (s_(f)/u_(f)/s_(i)/u_(i)). Thus, enrichment is dependent ondepleting the unselected particles but also on maintaining high yieldsof the selected particles (s_(f)/s_(i)). In the systems describedherein, enrichment ratios of 8-∞ corresponded to yields of 60%−5%, aftera single pass. An enrichment ratio of ∞ corresponds to zero unselectedparticles present in the filtrate. The separation resolution is ameasure of the size difference required for successful separation (asmaller number is better). It is defined as the size difference requiredfor >90% depletion of the unselected particles, divided by thefractional yield of selected particles. Using FIG. 24B, in oneembodiment, a single pass provides for 1 log enrichment in separation ofparticles with 3-μm resolution.

Example 16

Referring now to FIGS. 32A-32B, in one embodiment, a system is providedfor focusing particles above a certain size while smaller particlesremain unfocused for a given geometry. To investigate the relationshipbetween particle size and channel geometry, a mixture of 10-μm and 2-μmbeads were flown at varying flow rates through a channel having anexpanding spiral configuration. As can be seen in FIGS. 32A and 32B, thesmaller 2-μm particles remain unfocused, while the 10-μm particlesquickly focus and remain focused at different turns of the spiral. Wetested different flow rates and the 2-μm particles remained unfocusedirrespective of flow rate, supporting the theory of a optimal particlesize to channel geometry below which no focusing can occur. High-speedcamera result shown in FIG. 32B illustrate that the larger 10-μmparticles are focused in a single stream very close to the inner wall,while the 2-μm particles are scattered all over the channel.

The larger 10-μm particles remain focused over a wide range of R_(c) dueto the dominant lift forces balancing the secondary Dean flow pushingthe particles to the outer wall. The larger 10-μm particles are focusedcloser to the inner wall, enabling almost 100% recovery of the enriched10-μm particles fraction. The focusing of particles is not limited torigid particles, but also non-rigid biological material. Cells were alsosuccessfully focused to single streams, opening up opportunities forhigh throughput processing of biological components.

Example 17

To test the effect of R_(c) on the lateral positional displacement offocused particles within a spiral channel, 10-μm particles were flown ata large range of flow rates (0.1-5.5 mL/min) for given channel geometryand radius of curvature. As illustrated in FIGS. 33A-33C, particlesremain focused over a wide range of R_(c), and the focused particletrains are progressively displaced laterally away from the inner wallwith increased R_(c). These results support the theory and indicate theimportant role the secondary Dean flow plays in influencing the lateraldisplacement of single-stream focused particles over a wide range ofR_(c). As the R_(c) is increased beyond a certain value for a givenchannel geometry and particle size, the Dean drag becomes more dominantthan inertial lift and the single stream focused particles start todrift away from the inner wall to form multiple-stream band of focusedparticles, as shown in FIG. 33B. Further increase in R_(c) leads tocomplex fluid behavior disrupting the band and mixing. This suggeststhere is an upper limit on D_(e) above which particles start to mix dueto dominant Dean flow. In addition to D_(e), particle size to channelgeometry ratio and radius curvature is a strong influence on particlebehavior.

To investigate the relationship between various parameters affectingfocusing of particles, different flow experiments with varying particlesizes and channel geometries were conducted. We tested a range ofparticle diameters (2-15-μm) and channel geometries (D_(h) 55-183-μm andradius of curvature 1.4-9.5 mm) for R_(c) values ranging from 4 to 700.FIG. 33C shows the results of lateral displacement of focused particlesplotted as a function R_(f) for the different conditions tested. Thedata is normalized and all calculations were based on n=−0.43. Theresults indicate that, although the magnitudes differ, the variousparameters affect the balance of Drag forces and inertia lift in similarfashion, which is in good agreement with the theoretical prediction.High value on the y-axis indicate F_(z)>>F_(drag), resulting in smallerlateral displacement of the focused particles from the inner wall. Thisis accomplished by focusing a particular particle size at low R_(c) orby increasing the radius of curvature for a given R_(c). Increase inR_(c) or decrease in radius of curvature result in lateral displacementaway from the inner wall.

To investigate lateral displacement of focused particles in detail,different particle sizes were mixed and tested at various flow rates. Atlow flow rates, 10-μm and 7-μm particles are focused at the samestreamline, indicative of inertia lift dominating over Dean drag, asshown in FIGS. 34A and 34B. As R_(c) increases, both particle sizes arepushed away from the inner wall, in agreement with an increasedcontribution from Dean drag that is predicted, as discussed earlier.However, the smaller particles are affected more by the increase inR_(c) in comparison to the larger particles and consequently drift awayinto a new equilibrium position further away from the inner wall. Thisnew equilibrium position is independent of the presence of largerparticles. Thus for a given channel geometry and R_(c), the particleswill always focus at a predicted equilibrium position.

Example 18

Referring to FIGS. 35A-35F, separation applications based ondifferential equilibrium displacement within a spiral microfluidicdevice can be demonstrated. A cocktail mixture of particles (10, 7, 5and 3-μm) were flown through a microfluidic spiral device with a channeldepth of 50-μm with two outlets. One of the outlets was a channel of50-μm wide and the other one was 950-μm. According to the theory andexperimental findings, this specific dimension should allow the 10, 7and 5-μm beads to focus while the 3-μm beads remain unfocused for anygiven R_(c). As shown in FIGS. 32A-32F, increasing the flow rate pushesthe 7 and 5-μm beads away from the inner wall, while the 10-μm beads areintact focused in a single streamline closest to the inlet and can beeffectively separated. In this exemplary system, close to 100%separation of 10-μm beads is provided, as shown in FIG. 35F, at a flowrate of 3.5 ml/min.

Example 19

FIG. 36 illustrates utilizing inertial focusing for particle separation.An input solution of 0.1% w/v of mean diameter 3.87 μm (4) and 7.32 μm(7), uniformly distributed, was introduced into a single asymmetricdevice 100 (narrow)-160 (wide) μm in width, 50 μm tall, and 3 cm inlength. At the outlet the channel was split into 5 exit channels withequivalent resistance and fractions were collected for a flow at Re˜8.Flow of a total of 1 mL of solution over 10 minutes allowed ample samplefor analysis by coulter counter. Histograms of particle sizes are shownfor each of these fractions (numbers 1-5 and indicated in the image).The volumetric ratio between 4 (3-5 μm) and 7 (6-8.5 μm) micrometerparticles is shown above each histogram. Notably in fraction 2 thelarger particles are enhanced two-fold while in fraction 5 the largerparticles are depleted ˜200 times.

Example 20

FIG. 37 illustrates focusing behavior in symmetric curving channels. AsR_(e) number increases from 0.5 to 5 a transition to two focused streamsis observed. As R_(e) is increased further stable but more complexbehavior is observed. Scale bar is 50 μm.

Example 21

FIG. 38 illustrates the dependence of particle focusing on a/D_(h).Streak images at the outlet are shown 3 cm downstream of the inlet for aflow at Re=100. The image is shown at the recombination of two branchesto illustrate the uniformity of the flow profile from channel tochannel.

Example 22

FIG. 39 illustrates focusing behavior for channels of 35 μm to 65 μmwidth. The average radius of curvature for the small dimension is 32.5μm. Focusing to a single stream is observed ˜R_(e) of 5 while focusingto two streams is observed at higher R_(e) and at lower Re number. Theparticle diameter is 10 μm. Scale bar is 50 μm.

Example 23

FIG. 40 illustrates focusing behavior for channels of 50 μm to 80 μmwidth. The average radius of curvature for the small dimension is 40 μm.Focusing to a single stream is observed ˜R_(e) of 2.5 while focusing totwo streams is observed at higher R_(e). Above R_(e)=25 more complex butstable behavior is observed. The particle diameter is 10 μm. Scale baris 50 μm.

Example 24

FIG. 41 illustrates focusing behavior for channels of 100 μm to 160 μmwidth. The average radius of curvature for the small dimension is 80 μm.Focusing to a single stream is observed ˜R_(e) of 12 while more complexbut stable behavior is observed for higher R_(e). The particle diameteris 10 μm. Scale bar is 100 μm.

Example 25

FIG. 42 illustrates focusing behavior for channels of 350 μm to 650 μmwidth. The average radius of curvature for the small dimension is 325μm. Focusing to a single stream is observed ˜R_(e) of 90 while morecomplex but stable behavior is observed for higher R_(e). The particlediameter is 10 μm. Scale bar is 100 μm.

Example 26

FIG. 43 illustrates particle dependent focusing for separation. Auniform mixture 10 μm and 2 μm particles was input at the inlet andfluorescent streak images were observed at the outlet for (A) the greenfluorescent 10 μm particles and (B) the red fluorescent 2 μm particles.The flow is at a R_(e) of 5. There is a distinct separation acrossstreamlines for the different size particles with no externally appliedforces. The scale bar is 50 μm.

Example 27

FIG. 44 illustrates focusing of blood cells in the same manner as rigidparticles. Five percent whole blood diluted in PBS is run throughrectangular channels of 50 μm width. At the outlet, 3 cm downstream,streak images of cells are observed in phase contrast. These appear asdark streams in the gray channel. The channel edges are also dark. As inthe case with rigid particles 3 streaks are observed which correspond tofour focus points on the rectangular channel faces.

Example 28

FIGS. 45A and 45B illustrate focusing of cultured cell lines. As withparticles, deformable cells are focused to single streams. FIG. 43Ashows streak images of cells focusing for various R_(e) numbers areshown. The inlet of each focusing area is shown on the left. Focusing toa single lane starts to occur for R_(e) ˜2 after 3 cm of travel. In FIG.43B, intensity cross sections at various turns and at the outlet areshown. Note that at the outlet the width of the focused stream iscomparable to the diameter of a single cell (˜15 μm).

Experimental Conditions and Apparatus

While many experimental conditions can be used to create and utilize theexemplary systems described herein, some conditions used to achieve theresults discussed above are presented below.

Materials

Fluorescent polystyrene microparticles (density˜1.05 g/ml) were eitherpurchased from Bangs Laboratories (Fishers, Ind.) or Duke Scientific(Fremont, Calif.). For 4 (3.87) μm and 7 (7.32)μm particles the BangsLabs product codes were FS05F/7772 and FS06F/6316 respectively. For 2(2.0)μm, 9 μm, 10 (9.9)μm and 17 μm the Duke Scientific product numberswere R0200, 36-3, G1000 and 35-4. Particles were mixed to desired weightfractions by dilution in Phosphate buffered saline (PBS) and stabilizedby addition of 0.1% Tween 20. Particles were mixed to desired weightfractions by dilution in PBS and stabilized by addition of 0.1% Tween20. In the various described experiments particle wt/vol % variedbetween 0.1% and 1%. Silicone oil droplets were formed from 10% wt/volDC 200 (10 centistokes, Dow Corning) stabilized with 2% wt/volpolyethylene glycol monooleate (molecular weight 860, SigmaAldrich). Themixture was shaken vigorously and allowed to settle for 20 min. Solutionwas taken from the bottom 1 cm of the vial to ensure a size range ofdroplets <20-μm. Solutions of different densities were prepared fromethanol (p=0.78 g/ml) or concentrated CaCl₂ solutions (ρ=1.12 and 1.23g/ml); viscosities of these solutions varied from 1 to 3 centipoise.

Cells (H1650 lung cancer cell line) were cultured in RPMI 1640 mediawith 10% FBS and trypsinized and resuspended in PBS prior to use. Wholeblood was collected from a healthy volunteer in EDTA coated vacutainertubes by a trained phlebotomist. Blood was diluted in PBS to 1-5% forexperiments. Cells were dyed using either calcein AM (5 μM), acytoplasmic dye, or Hoescht 33342 (1 μM), which is a cell permeable DNAdye.

Microfabrication

Exemplary devices described herein were fabricated using standard softlithography techniques. Briefly, SU-8 2035 was spun at 2250 rpm for 30seconds to create a 50 μm thick layer on a 10 cm silicon wafer.Thickness was measured using a microscope with a metered focus andvaried between 42-56 μm across a wafer. The pattern wasphotolithographically defined in this layer using a mylar mask printedat 40,000 dpi (See Supplementary AutoCAD files). After development PDMSwas poured onto the SU-8 master at a 10 to 1 ratio of base tocrosslinker, degassed in a vacuum chamber, and cured at 65 degree C.overnight. The devices were then cut from the mold; ports were punchedwith a sharpened flat tip needle, and then bonded to glass slides orcover glass using oxygen plasma. After plasma treatment and placementonto the glass substrate the devices were maintained at 70 degree C. ona hotplate for 15 minutes to increase bonding.

Dimensionless Numbers

For a straight rectangular channel the Re, a ratio between the inertialand viscous forces can be easily defined as pUD_(h)/μ where ρ is thedensity of the fluid, U is the mean velocity, and D_(h), the hydraulicdiameter, is defined as 2ab/(a+b). With a and b being the width andheight of the channel. However, for curving channels and asymmetriccurving channels taking only a rectangular cross-section and consideringthe R_(e) for this will overestimate the inertial effects. In order todefine a correct R_(e) for these geometries fluid dynamic simulationswere conducted of the geometry using COMSOL Multiphysics. A R_(e) wasdetermined from the balance of inertial to viscous forces for nodepoints within the middle of the stream. This method yielded theanalytical R_(e) for straight rectangular channels as well. In the caseof the asymmetric channels the R_(e) differs in the small or largecurving turn and for simplicity a single R_(e) was used corresponding tothe small turn throughout this work. As an example an average velocityof 42 cm/sec corresponds to a R_(e) of 5 in a 50 μm×50 μm small curvingchannel of radius of curvature, r=40 μm, while R_(e)=20 for a straightrectangular channel. Dean numbers were also calculated using thesesimulated R_(e).

Particle Localization

The bias and accuracy of localization based on fitting to a functionalform will depend on the pixel size (i.e. the level of sampling) and thesignal to noise of the system (S/N). S/N is defined as,S/N=(I_(o)−I_(b))/σ_(o), that is the average intensity of the backgroundsubtracted from the average intensity of the object and divided by thestandard deviation or noise over the object. This is the highest noiseregion due to shot noise being proportional to the square root of thenumber of photoelectrons. For the system, with highly dyed fluorescentmicrospheres the S/N was determined to be 60 by taking the standarddeviation of intensity levels of a single stream over distance. This isin contrast to systems imaging single molecules which have typical S/Nof 4-10. For the signal to noise ratio and a pixel sampling size of 330nm, a predicted accuracy of localization of ˜3 nm is expected. Thisresult allows confidence in localization measurements that are largerthan this value by around an order of magnitude.

Image Analysis

For flow cytometry applications and to determine autocorrelationfunctions for flowing streams of particles Matlab (The Mathworks Inc.)was used to conduct image analysis of sequences of images. First, foreach movie a kernel image was selected that was representative of an infocus particle. This kernel was then convolved with the image to form anintensity map with peaks at particle positions. A defined section ofthis intensity map that corresponded to the distance a particle traveledin a given frame was converted to a time series of intensity andappended onto an array with time series from previous frames. Thisprocess was repeated for each frame until a full time series wasassembled of particle flow through the detection area. The temporalsignal was used to determine an autocorrelation function to analyze thefavored distances between particles and length of trains. It should benoted that convolution will necessarily increase the apparent width of agiven particle, but was conducted to obtain single peaks at particlepositions from the multiple intensity peak raw data.

Experimental Setup

As described herein, experiments to determine the distribution ofparticle positions within the channels were performed using time lapsefluorescence microscopy. Solutions were introduced into a syringe andconnected by PEEK tubing to the PDMS devices. In one embodiment, thesystem included a filter region to remove any large debris, curvingseparation microchannels, and five collection outlets, as shown in FIG.33. In other embodiments, the system included multiple inlets and asingle collection outlet. Outlets of PEEK tubing were also connected tothe outlet ports of the device and routed into a waste container orcollection tubes. Flow was driven by a syringe pump (Harvard ApparatusPHD 2000). In one embodiment, curving channels having a width of 350-μmon the small radius of curvature turn and a width of 650-μm on the largeradius of curvature turn were used. The average radius of curvature onthe narrow and wide turns is 325 and 890-μm, respectively. This geometryresults in an asymmetric system with a Dean drag (F_(D)) that is ˜8times larger in the small radius turn than in the large turn. In theillustrated embodiment, the entirety of the separation channel iscomposed of 31 units consisting of one small and one large turn, woundinto three straight segments (10-11 units each) to reduce the devicefootprint.

PDMS devices were mounted onto the stage of an inverted fluorescentmicroscope (Nikon TE2000-U). Fluorescent streak images were obtainedwith a cooled CCD camera (Spot RT, Diagnostic Instruments) usingexposure times from 500-5000 ms, depending on particle concentration andflow rate. Images were collected in the Spot software and furtheranalysis was conducted using ImageJ.

Confocal imaging was conducted in the same manner as invertedfluorescent imaging except devices were bonded to coverglass slides toallow objective access. A 40× objective was used with a pinhole diameterof 1.05 airy disks. The z-y plane was scanned 8 successive times with aresidence time of 0.3 ms at each scan point to obtain the images.

High-speed camera imaging was conducted in the same manner as invertedfluorescent imaging except white light in kohler illumination with theobject plane was utilized. All neutral density filters were removed andthe highest power on the lamp allowed imaging with 2 μs exposures usinga Phantom v4.2 camera (Vision Research, New Jersey, USA). For flowcytometry applications, images were collected at an interval of 10 μsusing a collection window that was 32×32 pixels. For larger singleimages and movies intervals from 20-70 μs were used.

After separating particle solutions into fractions, individual fractionswere analyzed using a Coulter counter (Beckman Coulter Z2). The coulteraperture size was 100 μm and gain and current were set to observeparticles in the size range of 3-9 μm. Collected samples were dilutedbetween 400 and 800 times to allow sufficient dilution for successfulcounting.

Blood cells were analyzed using a flow cytometer (Becton DickinsonFACSCalibur). Forward and side scatter were observed over a log scale todifferentiate between platelets and other blood components. Detectorvoltages were turned to obtain the correct gain to observe both thescatter of the larger and smaller particles. Samples were generallydiluted 100 times for measurements. 25,000-100,000 counts were observedfor each sample.

Emulsions

Silicone oil in water emulsions were generated by mixing of these twoimmiscible phases with emulsifier present in the aqueous (continuous)phase for stabilization from coalescence of the resulting oil droplets.Silicone oil with dynamic viscosity of 9.35 cP and density of 0.935g/cm³ was employed as the disperse phase (Dow Corning, Midland, Mich.;200 fluid 10 cst), while the continuous phase was composed of de-ionizedwater containing 2% w/v poly(ethylene glycol) monooleate (Sigma-Aldrich,St. Louis, Mo.; M_(n) ˜860) to stabilize the emulsion. After vigorousmixing of 5% v/v silicone oil with the aqueous phase, samples free ofdroplets larger than around 20-μm in diameter were obtained viasedimentation for subsequent experimentation. Specifically, emulsion wasextracted 1 cm from the bottom of evenly mixed emulsion that had beenallowed to stand for 20 minutes so that large droplets completelyevacuated the lower 2 cm of emulsion, as deduced from stokes drag on abuoyant spherical particle (v=D² (ρ_(aqu)−ρ_(oil)) g/(18η_(aqu))˜(3.55×10⁴ m⁻²s⁻¹) D²).

PDMS Beads

PDMS (Polydimethylsiloxane) beads with a wide range in diameter weremade in a fashion quite similar to silicone emulsions. PDMS was mixedwith the standard 10:1 ratio of resin to crosslinker (Dow Corning;Sylgard 184), but prior to curing, degassed resin-crosslinker mixturewas added to the same 2% w/v poly(ethylene glycol) monooleate aqueoussolution at 10% w/v PDMS. After vortex-mixing until the desired sizerange was achieved, the tube of uncured PDMS emulsion was placed in awater bath at 70-90° C. for at least three hours to allow hardening ofthe liquid droplets into solid beads of PDMS. Beads larger than about20-μm were removed from extracted solutions of beads prior to experimentvia filtration through a duplicate filter of a device as in FIG. 33.

In general, the embodiments disclosed herein present a nonintuitivephenomena associated with particles moving in a laminar flow that yieldsdifferent levels of ordering within microchannel systems. Ranges ofparameters are disclosed for utilization of the phenomena and keyprinciples and forces that may responsible for the ordering are alsosuggested. There are many advantages associated with the system of theinvention including rapid continuous processing of samples without theneed for filters or mechanical or electrical parts, high throughputapplications, low noise results, and an independence in focusing forparticle shape and density. Inertial focusing of the systems and methodsdescribed herein is ideal for particle sorting applications because ofthe precision of particle positioning into a single stream and thecontrolled longitudinal spacing between particles. Precise control ofparticle streamlines (i.e. small standard deviation of particleposition) allows sorting with small induced changes in particleposition. A slight induced movement of a particle away from theequilibrium streamline will yield a large difference over the backgroundstandard deviation of particle position and can allow the targetparticle to be extracted at a bifurcation in the channel without highlevels of false positives and at high speeds. Additionally, the singlefile nature of the ordering and the regular longitudinal spacing insuresthat a deflected particle would not interact significantly with otherparticles in the flow. The particular geometries presented can be usedin any number of applications to direct interactions of particles ininertial flows, and the system of the invention is applicable on amicroscale as well as on a macroscale. It is appreciated that any andall channel geometries, system embodiments, and experimental parametersdescribed herein can be combined in a multitude of ways to achievespecific results in various applications.

Applications of the system of the invention are widely diverse and willbe useful in a wide range of industries, both commercial and academic.For example, in the biomedical field, applications of the system can beused in conventional techniques such as FACS, MACS, impedance-basedparticle counting, blood filtration, rare cell identification andfiltration, hetero/hemogenous cell signaling, among many others. Forexample, the properties of the particle motion induced by inertialfocusing are ideally suited to cell separation and enumerationtechnologies. The extreme alignment and discrete spacing of each cellcan be exploited to enumerate the cells individually as they flowthrough a microfluidic channel at high speeds by, for example, labelingcells with fluorescent tags or magnetic particles. The systems andmethods described herein have many advantages over current rare-cellseparation and enumeration techniques. Immunomagnetic techniques—wherecells of interest are tagged with antibody coated magnetic beads—areoften employed, however, cell losses occur in the processing of thesesamples because of its complexity and manual handling steps. A furtheradvantage of the systems and methods is the ability to perform the cellordering and separation at the point of care without the need for bulkyequipment that is only suitable for the laboratory setting. Particlefocusing techniques such as those described here can be combined withestablished immunomagnetic labeling and microelectronics technology todesign and construct an cell separation microchip, for example, capableof handling whole blood samples that will not suffer from the problemsof the current technologies. Microelectronic components can beintegrated into microfluidic devices and therefore combine fluid flowand electronic manipulation or detection in a single device. The systemsand methods described herein will create opportunities for the rapidscreening of patients for a number of diseases and allow clinicians tofollow the treatment progress of their patients.

In other applications, for example in industry, possible applications ofthe systems and methods of the invention can include use in thedevelopment of cosmetics, lubricants, pigments, environmental monitoringfor particulates, natural oil extraction, particle synthesis, andpolymer bead manufacturing, among many others. In research, the systemof the invention can be used in tissue engineering, drug control releasemechanism studies, cell signaling studies, protein crystallization,virus/bacteria capture, nucleic acid purification, and chemistryspecific extractions among many others. In the field of agriculture, thesystem of the invention can find application in the development ofmulti-phase fertilizer emulsions, multi-phase pesticide emulsions, flowcytometry, as well as in hematology analysis. The possible applicationsfor the systems and methods of the invention are varied and broad acrossall research, industrial, and commercial applications.

One skilled in the art will appreciate further features and advantagesof the invention based on the above-described embodiments. Accordingly,the invention is not to be limited by what has been particularly shownand described, except as indicated by the appended claims. Allpublications and references cited herein are expressly incorporatedherein by reference in their entirety.

What is claimed is: 1-196. (canceled)
 197. A method of focusingparticles suspended in a fluid, the method comprising: adding tags toparticles suspended in a fluid to change a size of the particles; andflowing the fluid and the tagged particles through a system comprising:a substrate; and at least one channel provided on the substrate, whereinthe at least one channel has an inlet, an outlet, and a plurality ofsides defining an aspect ratio and a channel hydraulic diameter (D_(h)),wherein the at least one channel is dimensioned and configured to allowthe fluid having a kinematic viscosity (ν) and including suspendedtagged particles, each having a particle diameter (a), to flowtherethrough such that, when the fluid is flowed therethrough at amaximum channel velocity (U_(m)) resulting in laminar fluid flow and aparticle Reynolds Number (R_(p)) of greater than or equal to 0.2,wherein the particle Reynolds number is defined as${R_{p} = \frac{U_{m}a^{2}}{{vD}_{h}}},$ the tagged particles suspendedin the fluid are focused to flow along one or more localized streamlines that form in the fluid of the at least one channel.
 198. Themethod of claim 197, wherein the tags comprise beads.
 199. The method ofclaim 197, wherein the tags comprise antibodies.
 200. The method ofclaim 197, wherein the tags comprise magnetic beads.
 201. The method ofclaim 197, wherein the tags comprise quantum dots.
 202. The method ofclaim 197, further comprising focusing the tagged particles into aparticular stream line based on the changed size.
 203. The method ofclaim 197, wherein the system further comprises a channel branch andwherein the method further comprises focusing the tagged particles intothe channel branch based on the changed size.
 204. The method of claim197, wherein the one or more localized stream lines each define a widththat is substantially equal to or greater than the diameter of thetagged particles, and the tagged particles suspended in the fluid arefocused into the one or more localized stream lines, and wherein thenumber and relative cross-sectional position of the one or morelocalized stream lines are uniquely defined by the aspect ratio and theparticle Reynolds number.
 205. The method of claim 197, wherein thetagged particles suspended in the fluid are focused into each of atleast two localized stream lines.
 206. The method of claim 197, furthercomprising a curved channel connected to the outlet of the at least onechannel, wherein when the fluid is flowed through the at least onechannel and the curved channel, the tagged particles are focused into asingle localized stream line formed in the curved channel.
 207. Themethod of claim 206, wherein the curved channel is sigmoidal.
 208. Themethod of claim 197, wherein a ratio of the tagged particle diameter tothe at least one channel hydraulic diameter is greater than or equal toabout 0.07 and less than or equal to about 0.5.
 209. The method of claim197, wherein the at least one channel is dimensioned and configured tofocus tagged particles having a diameter in a range of 0.01 micrometersto 40 micrometers.
 210. The method of claim 197, wherein the at leastone channel has a width and a height that defines the aspect ratio ofthe at least one channel, and wherein the aspect ratio is 1 at orsubstantially near the inlet and varies over the length of the at leastone channel to 2 at or substantially near the outlet.
 211. The method ofclaim 197, further comprising a filter positioned upstream of, and influid communication with, the at least one channel, wherein the filterhas a cut-off size selected to prevent passage of tagged particleslarger than the hydraulic diameter of the at least one channel.
 212. Amethod of focusing particles suspended in a fluid, the methodcomprising: adding tags to the particles suspended in a fluid to changea size of the particles; and flowing the fluid and the tagged particlesthrough a system comprising: a substrate; and at least one channelprovided on the substrate, wherein the at least one channel spans alength from an inlet to an outlet and has a channel hydraulic diameter(D_(h)), and comprises a plurality of curves, wherein the at least onechannel is dimensioned and configured to allow a fluid having akinematic viscosity (ν) that includes suspended tagged particles, eachhaving a particle hydraulic diameter (a), to flow therethrough such thatwhen the fluid is flowed therethrough at a maximum channel velocity(U_(m)) resulting in laminar fluid flow and a particle Reynolds Number(R_(p)) of greater than or equal to 0.2, wherein the particle Reynoldsnumber is defined as ${R_{p} = \frac{U_{m}a^{2}}{{vD}_{h}}},$ thetagged particles suspended in the fluid are focused to flow along one ormore localized stream lines that form in the fluid at the outlet of theat least one channel.
 213. The method of claim 212, wherein the tagscomprise beads.
 214. The method of claim 212, wherein the tags compriseantibodies.
 215. The method of claim 212, further comprising focusingthe particles into a particular stream line based on the changed size.216. The method of claim 212, wherein the system further comprises achannel branch and wherein the method further comprising focusing theparticles into the channel branch based on the changed size.